V = Bh. Here B is the area of the triangle, and h is the length of the prism.
Step-by-step solution
The bases are the triangles. Area of one triangle: B = \tfrac{1}{2}bh = \tfrac{1}{2}(6)(4) = 12\text{ in}^2.
The distance between the triangles (the prism's height) is 10\text{ in}.
V = Bh = 12 \times 10 = 120.
The volume is 120\text{ in}^3.
Check: the box around this prism would be 6 \times 4 \times 10 = 240\text{ in}^3; a triangle is half a rectangle, so the prism is 240 \div 2 = 120 ✓.
Tip: Find the shape on the two matching ends first and get its area. Then multiply by the length of the prism.
Question 2 of 36
Fill in
A glass paperweight is a prism with a hexagon-shaped base. The area of the hexagon is 24\text{ cm}^2, and the prism is 7\text{ cm} tall.
What is the volume of the paperweight?
\text{cm}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
You don't need a hexagon formula. The base area B is already given; use V = Bh.
Step-by-step solution
For every right prism, V = Bh.
The base area is given: B = 24\text{ cm}^2.
The height of the prism (distance between the two hexagons) is h = 7\text{ cm}.
V = 24 \times 7 = 168.
The volume is 168\text{ cm}^3.
Check:168 \div 7 = 24, the base area we were given ✓.
Tip:V = Bh works for prisms with any base shape: triangle, trapezoid, hexagon, even an irregular shape. If the problem gives you B, skip straight to multiplying.
Question 3 of 36
Find the surface area of the triangular prism shown.
Hint
SA = ph + 2B, where p is the perimeter of the triangle and B is its area.
Step-by-step solution
Perimeter of the triangle: p = 3 + 4 + 5 = 12\text{ cm}.
Lateral area (the three rectangles): ph = 12 \times 10 = 120\text{ cm}^2.
Area of one triangle (legs 3 and 4): B = \tfrac{1}{2}(3)(4) = 6\text{ cm}^2, so 2B = 12\text{ cm}^2.
Tip: In a right triangle, the two legs are the base and height. The hypotenuse 5 goes into the perimeter but not into B.
Question 4 of 36
A candy box is a triangular prism, as shown.
What is the volume of the box?
Hint
The base of this prism is a triangle. Find its area with \tfrac{1}{2}bh, then multiply by the length.
Step-by-step solution
The bases are the two triangular ends. Area of one triangle: B = \tfrac{1}{2} \times 4 \times 3.5 = 7\text{ cm}^2.
The prism's length is the distance between the triangles: 20\text{ cm}.
V = Bh = 7 \times 20 = 140.
The volume is 140\text{ cm}^3.
Check: a box around the prism would be 4 \times 3.5 \times 20 = 280\text{ cm}^3; a triangular prism is exactly half of it, and 280 \div 2 = 140 ✓.
Tip: For any prism, V = Bh: first the area of the base shape, then times the length. For a triangle base, the \tfrac{1}{2} is easy to forget.
Question 5 of 36
Fill in
A decorative candle is a prism whose base is a pentagon. The area of the pentagon is 35\text{ in}^2, and the candle is 12\text{ in} tall.
What is the volume of the candle?
\text{in}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
You don't need a pentagon formula. The area of the base is already given; use V = Bh.
Step-by-step solution
For every prism, V = Bh, where B is the area of the base.
Here B = 35\text{ in}^2 (given) and h = 12\text{ in}.
V = 35 \times 12 = 420.
The candle's volume is 420\text{ in}^3.
Check:420 \div 12 = 35, the base area ✓.
Tip: When the problem hands you the base area, the shape of the base no longer matters. The formula V = Bh works for prisms with any polygon base, and it is on the GED formula sheet.
Question 6 of 36
A glass prism used in a science class has equilateral-triangle ends. Each side of a triangle is 6\text{ cm}, the height of each triangle is about 5.2\text{ cm}, and the prism is 10\text{ cm} long.
What is the total surface area of the prism?
Hint
Add the two triangles and the three rectangles. The three rectangles together are (perimeter of the triangle) × length.
Step-by-step solution
One triangle: \tfrac{1}{2} \times 6 \times 5.2 = 15.6\text{ cm}^2. Two triangles: 31.2\text{ cm}^2.
Perimeter of the triangle: 6 + 6 + 6 = 18\text{ cm}.
Three rectangles (lateral area): 18 \times 10 = 180\text{ cm}^2.
Total: 31.2 + 180 = 211.2.
The surface area is 211.2\text{ cm}^2.
Check: each rectangle is 6 \times 10 = 60, and 3 \times 60 = 180 ✓; plus two triangles of 15.6 gives 211.2 ✓.
Tip: The formula sheet's SA = ph + 2B works for triangular prisms too: p is the perimeter of the triangle, h is the length of the prism.
Question 7 of 36
A camping tent is shaped like the triangular prism shown. The tent has no floor.
How many square feet of canvas are needed to make the tent (the two triangular ends and the two slanted sides)?
Hint
List the faces that are really made of canvas: 2 triangles and 2 slanted rectangles. The floor rectangle is not included.
Step-by-step solution
Each triangular end: \tfrac{1}{2}(8)(3) = 12\text{ ft}^2. Two ends: 24\text{ ft}^2.
Each slanted side is a rectangle 5\text{ ft} by 10\text{ ft}: 50\text{ ft}^2. Two sides: 100\text{ ft}^2.
No floor, so the 8 \times 10 rectangle is left out.
Canvas: 24 + 100 = 124.
The tent needs 124\text{ ft}^2 of canvas.
Check: the full surface area would be ph + 2B = (5 + 5 + 8)(10) + 24 = 180 + 24 = 204; subtract the 80\text{ ft}^2 floor: 204 - 80 = 124 ✓.
Tip:SA = ph + 2B counts every face. When something is open or missing, add up only the faces that exist, or subtract the missing one.
Question 8 of 36
Fill in
The triangular prism shown has a volume of 270\text{ in}^3.
What is the length L of the prism, in inches?
L = in
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Find the area of the triangle first. Then use V = Bh and solve for the length.
Step-by-step solution
Area of the triangular base: B = \tfrac{1}{2}(9)(6) = 27\text{ in}^2.
Tip: Working backwards from volume: divide the volume by the base area (not by one side). Forgetting the \tfrac{1}{2} here would give 270 \div 54 = 5, which is half the correct length.
Question 9 of 36
Drop-down
A farmer's water trough is a prism with trapezoid-shaped ends, as shown.
Select the correct value for each blank.
The area of one trapezoid end is , and the trough holds of water when full.
Choose an answer from each menu.
Hint
The trapezoid area formula is on the formula sheet: A = \tfrac{1}{2}h(b_1 + b_2). Then V = Bh with the trough's length.
Step-by-step solution
The bases of the prism are the trapezoids. b_1 = 2, b_2 = 4, trapezoid height 1.5.
B = \tfrac{1}{2}(1.5)(2 + 4) = \tfrac{1}{2}(1.5)(6) = 4.5\text{ ft}^2.
The prism's height is the trough's length, 8\text{ ft}.
V = Bh = 4.5 \times 8 = 36\text{ ft}^3.
The end has area 4.5\text{ ft}^2 and the trough holds 36\text{ ft}^3.
Check: the average width is (2 + 4) \div 2 = 3\text{ ft}, and 3 \times 1.5 \times 8 = 36 ✓.
Tip: Add the two parallel sides before multiplying: \tfrac{1}{2} \times 1.5 \times (2 + 4). Parentheses on the calculator keep this in order.
Question 10 of 36
A wooden ramp is a triangular prism lying on one of its rectangular faces, as shown.
What is the volume of the ramp?
Hint
The bases are the two matching triangles on the ends, even though the prism rests on a rectangle. Which two sides of a right triangle are perpendicular?
Step-by-step solution
The two matching ends are right triangles, so they are the bases.
The legs 5 and 12 are perpendicular, so they are the triangle's base and height: B = \tfrac{1}{2}(12)(5) = 30\text{ in}^2.
The distance between the triangles is 20\text{ in}.
V = Bh = 30 \times 20 = 600.
The volume is 600\text{ in}^3.
Check: the box around the ramp is 12 \times 5 \times 20 = 1{,}200; the ramp is half of it: 600 ✓.
Tip: The hypotenuse (13) is never the height of a right triangle. Use the two legs for B; use the hypotenuse only for perimeter or surface area.
Question 11 of 36
Select all
Use the triangular prism shown.
Select all statements that are true.
Select all that apply.
Hint
Find B (use the legs), p (all three sides), then V = Bh, the lateral area ph, and SA = ph + 2B.
Step-by-step solution
B = \tfrac{1}{2}(9)(12) = 54\text{ cm}^2; p = 9 + 12 + 15 = 36\text{ cm}; h = 10\text{ cm}.
Volume: V = 54 \times 10 = 540\text{ cm}^3. A is true.
Lateral area: ph = 36 \times 10 = 360\text{ cm}^2. C is true.
Surface area: SA = 360 + 2(54) = 360 + 108 = 468\text{ cm}^2. E is true.
B (1{,}080) forgets the \tfrac{1}{2}; D (414) adds only one triangle (360 + 54). Both false.
Tip: Organize your work as B, p, h first. Every statement in a select-all prism question is built from those three numbers.
Question 12 of 36
Drag and drop
Drag each prism into the column that shows its volume. One prism will not be used.
V = 60\text{ cm}^3
V = 90\text{ cm}^3
V = 120\text{ cm}^3
Tap a tile, then tap a box to place it.
Hint
For each prism find the base area B (triangle: \tfrac{1}{2}bh; trapezoid: \tfrac{1}{2}h(b_1 + b_2)), then multiply by the length.
Step-by-step solution
Triangle base 4, height 3, length 10: B = \tfrac{1}{2}(4)(3) = 6; V = 6 \times 10 = 60 → 60\text{ cm}^3.
Trapezoid with parallel sides 2 and 4, height 3, length 10: B = \tfrac{1}{2}(3)(2 + 4) = 9; V = 9 \times 10 = 90 → 90\text{ cm}^3.
Hexagon with area 12\text{ cm}^2, height 10: V = 12 \times 10 = 120 → 120\text{ cm}^3.
Triangle base 4, height 3, length 5: B = 6, V = 6 \times 5 = 30\text{ cm}^3 → matches no column, not used. (Forgetting the \tfrac{1}{2} gives 60 — the trap.)
Tip: Different base shapes, same method: area of the end × length. Write B for each before multiplying.
Question 13 of 36
Fill in
A kids' play fort is shaped like a triangular prism with no floor. Each triangular end has a base of 10\text{ ft}, a height of 12\text{ ft}, and two slanted sides of 13\text{ ft}. The fort is 15\text{ ft} long.
How many square feet of fabric cover the two triangular ends and the two slanted sides?
\text{ft}^2
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Picture the fort: two triangles and two slanted rectangles. The bottom rectangle (the floor) is missing.
Step-by-step solution
One triangular end: \tfrac{1}{2} \times 10 \times 12 = 60\text{ ft}^2. Two ends: 120\text{ ft}^2.
One slanted side: 13 \times 15 = 195\text{ ft}^2. Two sides: 390\text{ ft}^2.
Total: 120 + 390 = 510.
The fort needs 510\text{ ft}^2 of fabric.
Check: with a floor it would also need 10 \times 15 = 150\text{ ft}^2, giving 660. Removing the floor: 660 - 150 = 510 ✓.
Tip: The slanted rectangles use the slanted side (13), not the height (12). The height is used only inside the triangle's area.
Question 14 of 36
A wooden doorstop is a triangular prism with a volume of 336\text{ in}^3. The prism is 14\text{ in} long, and the base of each triangle is 8\text{ in}.
What is the height of each triangle?
Hint
Write V = \tfrac{1}{2} \times b \times h \times L with the numbers you know, simplify, and solve for h.
Step-by-step solution
V = \tfrac{1}{2}bhL \Rightarrow 336 = \tfrac{1}{2} \times 8 \times h \times 14.
Simplify the known numbers: \tfrac{1}{2} \times 8 \times 14 = 56.
Tip: Combine every known number (including the \tfrac{1}{2}) into one coefficient first. Then a single division finishes the problem.
Question 15 of 36
A wooden planter is a prism with trapezoid-shaped ends. Each end has a bottom of 10\text{ in}, a top of 16\text{ in}, and a height of 9\text{ in}. The planter is 30\text{ in} long.
How much soil does the planter hold when full?
Hint
Area of a trapezoid: \tfrac{1}{2}(b_1 + b_2)h. Then multiply by the length.
Step-by-step solution
Area of one trapezoid end: B = \tfrac{1}{2}(10 + 16)(9) = \tfrac{1}{2}(26)(9) = 117\text{ in}^2.
Volume: V = Bh = 117 \times 30 = 3{,}510.
The planter holds 3{,}510\text{ in}^3 of soil.
Check: the planter must hold more than a 10 \times 9 \times 30 = 2{,}700 box and less than a 16 \times 9 \times 30 = 4{,}320 box. 3{,}510 is right in the middle ✓.
Tip: A trapezoid's area uses the average of the two parallel sides: \tfrac{10 + 16}{2} = 13, and 13 \times 9 = 117. The trapezoid formula is on the GED formula sheet.
Question 16 of 36
Drop-down
A concrete ramp is a triangular prism lying on its bottom rectangle, as shown.
Select the correct choice for each blank.
In V = Bh, the base B is the area of . The volume of the ramp is .
Choose an answer from each menu.
Hint
The bases of a prism are the two faces that match and are parallel, no matter which face the prism sits on.
Step-by-step solution
The two triangular sides are identical and parallel, so they are the bases, even though the ramp rests on a rectangle.
Base area: B = \tfrac{1}{2} \times 12 \times 1 = 6\text{ ft}^2.
The "height" of the prism is the distance between the triangles: the width, 4\text{ ft}.
V = Bh = 6 \times 4 = 24\text{ ft}^3.
The answers are one triangular side and 24\text{ ft}^3.
Check: a box with the same outside dimensions is 12 \times 1 \times 4 = 48\text{ ft}^3; the ramp is half of it ✓.
Tip: "Base" in a prism formula does not mean "the bottom". Look for the two matching faces — that shape gives B.
Question 17 of 36
Select all
A triangular prism has right-triangle ends with legs of 8\text{ cm} and 15\text{ cm} and a hypotenuse of 17\text{ cm}. The prism is 6\text{ cm} long.
Select all statements that are true.
Select all that apply.
Hint
Find the triangle's area (use the legs), the volume, the three rectangles, and the total surface area. Then test each statement.
Step-by-step solution
Base area: B = \tfrac{1}{2} \times 8 \times 15 = 60\text{ cm}^2. A is true.
Volume: V = 60 \times 6 = 360\text{ cm}^3. B is true.
Lateral area: (8 + 15 + 17) \times 6 = 40 \times 6 = 240\text{ cm}^2. C is true.
Surface area: 2(60) + 240 = 360\text{ cm}^2, so D (300, only one triangle) is false.
E (720) forgets the \tfrac{1}{2} in the volume. False.
Tip: In a right triangle the two legs are the base and height; the hypotenuse is used only for the perimeter (the lateral area).
Question 18 of 36
Drag and drop
A hobby shop sells small wooden blocks shaped like prisms. Sort the blocks by the amount of wood in each: drag every block into the column that shows its volume (measures in centimeters). One block will not be used.
V = 24\text{ cm}^3
V = 36\text{ cm}^3
V = 48\text{ cm}^3
Tap a tile, then tap a box to place it.
Hint
Find the area of each base shape (\tfrac{1}{2}bh for a triangle, \tfrac{1}{2}(b_1 + b_2)h for a trapezoid), then multiply by the length.
Step-by-step solution
Use V = Bh:
Triangle 4, 3: B = \tfrac{1}{2}(4)(3) = 6; V = 6 \times 4 = 24 → 24.
Triangle 6, 4: B = \tfrac{1}{2}(6)(4) = 12; V = 12 \times 4 = 48 → 48.
Triangle 2, 3: B = \tfrac{1}{2}(2)(3) = 3; V = 12 → not used.
Check: every volume divided by the length 4 gives the base area: 6, 9, 12 ✓.
Tip: The unused tile only "fits" the 24 column if you forget the \tfrac{1}{2}. Trap answers on the GED often come from exactly that slip.
Question 19 of 36
Fill in
A wedge of cheese is a prism with right-triangle ends. One leg of each triangle is 6\text{ cm}, and the hypotenuse is 10\text{ cm}. The wedge is 15\text{ cm} long.
What is the volume of the wedge?
\text{cm}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
To find the triangle's area you need both legs. Use the Pythagorean theorem to find the missing leg first.
Check: a rectangular trough 2 \times 1.5 \times 10 would hold 30\text{ ft}^3 = 225 gallons. The V-shape is half of that: 112.5 ✓.
Tip: Converting cubic feet to gallons means multiplying by 7.5 (each cubic foot holds 7.5 gallons, so gallons is the bigger number).
Question 22 of 36
Fill in
A wooden bookend is a triangular prism. Each triangular face has a base of 7.5\text{ cm} and a height of 6\text{ cm}. The bookend is 14\text{ cm} long.
What is the volume of the bookend?
\text{cm}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Triangle area first (\tfrac{1}{2}bh), then multiply by the length.
Tip: When a figure leaves a side unlabeled, the question usually expects the Pythagorean theorem. Watch for the 6-8-10 (a 3-4-5 doubled) right triangle.
Question 25 of 36
Fill in
The triangular prism shown has a volume of 960\text{ cm}^3. Each triangular base is isosceles, with two equal sides of 10\text{ cm} and a base of 12\text{ cm}.
What is the length L of the prism, in centimeters?
L = cm
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The triangle's height is not given. The height of an isosceles triangle cuts its base exactly in half, making two right triangles.
Step-by-step solution
The height of the triangle splits the 12\text{ cm} base into two halves of 6\text{ cm}, making right triangles with hypotenuse 10.
Pythagoras: h^2 + 6^2 = 10^2, so h^2 = 100 - 36 = 64 and h = 8\text{ cm}.
Base area: B = \tfrac{1}{2}(12)(8) = 48\text{ cm}^2.
Tip: A slanted side (10) is never the height. For an isosceles triangle, drop the height to the middle of the base, then use Pythagoras with half the base.
Question 26 of 36
The triangular prism shown has isosceles-triangle ends.
What is its total surface area?
Hint
Two triangles plus three rectangles. The three rectangles have widths 5, 5 and 6.
Step-by-step solution
One triangle: \tfrac{1}{2} \times 6 \times 4 = 12\text{ cm}^2. Two triangles: 24\text{ cm}^2.
Perimeter of the triangle: 5 + 5 + 6 = 16\text{ cm}.
Tip: The 4\text{ cm} height is used only for the triangle's area. The rectangles use the triangle's sides (5, 5, 6).
Question 27 of 36
A skateboard ramp is a triangular prism. Each triangular side is a right triangle with a rise of 3\text{ ft}, a run of 4\text{ ft} and a slanted top of 5\text{ ft}. The ramp is 6\text{ ft} wide.
The builder covers only the two triangular sides and the slanted top with plywood (not the bottom or the vertical back). How many square feet of plywood are needed?
Hint
List the faces to cover: two triangles and one 5 \times 6 rectangle.
Step-by-step solution
One triangle: \tfrac{1}{2} \times 4 \times 3 = 6\text{ ft}^2. Two triangles: 12\text{ ft}^2.
Slanted top: 5 \times 6 = 30\text{ ft}^2.
Total: 12 + 30 = 42.
The builder needs 42\text{ ft}^2 of plywood.
Check: the whole prism is 12 + (3 + 4 + 5) \times 6 = 12 + 72 = 84\text{ ft}^2. Remove the bottom (4 \times 6 = 24) and back (3 \times 6 = 18): 84 - 24 - 18 = 42 ✓.
Tip: In "missing face" problems, list every face of the solid, then cross out the ones the question excludes before adding.
Question 28 of 36
Fill in
A concrete curb is a prism with trapezoid-shaped ends. The parallel sides of each trapezoid are 5\text{ in} and 9\text{ in}. The curb is 10\text{ in} long and contains 420\text{ in}^3 of concrete.
What is the height of each trapezoid, in inches?
in
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Write V = \tfrac{1}{2}(b_1 + b_2) \times h \times L, simplify the known numbers, and solve for h.
Step-by-step solution
V = \tfrac{1}{2}(b_1 + b_2)h \times L \Rightarrow 420 = \tfrac{1}{2}(5 + 9) \times h \times 10.
\tfrac{1}{2}(14) = 7, and 7 \times 10 = 70, so 70h = 420.
Tip: Forgetting the \tfrac{1}{2} gives h = 3, and using only one parallel side gives other wrong values. Plug your answer back into the volume formula to be sure.
Question 29 of 36
Select all
A drainage ditch is a prism with trapezoid-shaped ends. The bottom of the ditch is 3\text{ ft} wide, the top is 7\text{ ft} wide, and the ditch is 2\text{ ft} deep. The ditch is 50\text{ ft} long. (One cubic foot holds about 7.5 gallons.)
Select all statements that are true.
Select all that apply.
Hint
Find the area of one end with the trapezoid formula, then the volume, then the gallons.
Step-by-step solution
End area: \tfrac{1}{2}(3 + 7)(2) = \tfrac{1}{2}(10)(2) = 10\text{ ft}^2. A is true; D (14) uses only the top width (7 \times 2) and is false.
Volume: 10 \times 50 = 500\text{ ft}^3. B is true; C (1{,}000) forgets the \tfrac{1}{2} and is false.
Gallons: 500 \times 7.5 = 3{,}750. E is true.
The true statements are A, B and E.
Check: the ditch is between a 3 \times 2 \times 50 = 300 box and a 7 \times 2 \times 50 = 700 box; 500 is exactly halfway ✓.
Tip: For a trapezoid, average the parallel sides (\tfrac{3 + 7}{2} = 5) and multiply by the height: 5 \times 2 = 10.
Question 30 of 36
A brass paperweight rests on its largest flat face on a desk. Its two matching ends are trapezoids: each has parallel sides of 8\text{ cm} (along the desk) and 5\text{ cm} (on top), and the distance between them is 3\text{ cm}. The paperweight is 10\text{ cm} long.
What is the volume of the paperweight?
Hint
Which faces match? Those trapezoids are the bases, even though the paperweight lies on a rectangle.
Step-by-step solution
The two trapezoid ends match, so they are the bases of the prism. The prism's "height" is the 10\text{ cm} length.
Base area: B = \tfrac{1}{2}(8 + 5)(3) = \tfrac{1}{2}(13)(3) = 19.5\text{ cm}^2.
Volume: V = 19.5 \times 10 = 195.
The volume is 195\text{ cm}^3.
Check: the paperweight is smaller than an 8 \times 3 \times 10 = 240 box and bigger than a 5 \times 3 \times 10 = 150 box; 195 is between ✓.
Tip: A prism lying on its side is the trap. Treating it as a box (8 \times 3 \times 10) ignores the slanted sides. Find the matching faces first.
Question 31 of 36
Two storage containers are compared.
Container A: a triangular prism whose triangle has a base of 6\text{ ft} and a height of 4\text{ ft}; its length is 10\text{ ft}.
Container B: a rectangular box 6\text{ ft} by 4\text{ ft} by 5\text{ ft}.
Which statement is true?
Hint
Compute both volumes with V = Bh. Remember the \tfrac{1}{2} for the triangle.
Step-by-step solution
Container A: B = \tfrac{1}{2}(6)(4) = 12\text{ ft}^2; V = 12 \times 10 = 120\text{ ft}^3.
Container B: B = 6 \times 4 = 24\text{ ft}^2; V = 24 \times 5 = 120\text{ ft}^3.
The volumes are equal.
They hold the same amount.
Check: A's base is half of B's (12 vs 24), but A is twice as long (10 vs 5). Half × double = the same ✓.
Tip: Comparing only base areas or only lengths gives half the picture. Volume depends on both.
Question 32 of 36
Drag and drop
A chocolate maker is choosing molds. Each mold is a prism, and its measures are in centimeters. Drag each mold into the column that shows how much chocolate it holds. One mold will not be used.
V = 42\text{ cm}^3
V = 60\text{ cm}^3
V = 70\text{ cm}^3
Tap a tile, then tap a box to place it.
Hint
In a right triangle the two legs are the base and height. For the trapezoid, average the parallel sides.
Step-by-step solution
Use V = Bh:
Legs 3, 4: B = \tfrac{1}{2}(3)(4) = 6; V = 6 \times 7 = 42 → 42.
Check: a box 10 \times 12 \times 12 (to the peak) would be 1{,}440; the shed is smaller because the two roof corners are missing: 1{,}440 - 2 \times \tfrac{1}{2}(5)(4)(12) = 1{,}440 - 240 = 1{,}200 ✓.
Tip: For an unusual base, split it into shapes you know (rectangles, triangles, trapezoids), add their areas to get B, and then use V = Bh as usual.
Question 34 of 36
A grain hopper is a triangular prism. Each triangular end has a base of 4\text{ ft} and a height of 3\text{ ft}, and the hopper is 9\text{ ft} long. One bushel of grain takes up about 1.25\text{ ft}^3.
About how many bushels of grain does the full hopper hold?
Hint
Find the volume in cubic feet, then find how many 1.25\text{ ft}^3 bushels fit in it.
Tip: Each bushel is more than one cubic foot, so the number of bushels must be smaller than the number of cubic feet. That tells you to divide, not multiply.
Question 35 of 36
Fill in
A swimming pool has a shallow end and a deep end. Its side view is shown; the pool is 15\text{ ft} wide.
How many cubic feet of water fill the pool to the top?
\text{ft}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The side view is the base of the prism. Split it into two rectangles, add their areas, then multiply by the width.
Step-by-step solution
Shallow part of the side view: 18 \times 3 = 54\text{ ft}^2.
Deep part: 12 \times 8 = 96\text{ ft}^2.
Base area: B = 54 + 96 = 150\text{ ft}^2.
Volume: V = Bh = 150 \times 15 = 2{,}250.
The pool holds 2{,}250\text{ ft}^3 of water.
Check: split it a different way: a 30 \times 3 top layer (90\text{ ft}^2) plus a 12 \times 5 deep pocket (60\text{ ft}^2) = 150\text{ ft}^2 ✓.
Tip: Using the whole 30 \times 8 rectangle (240\text{ ft}^2) counts water under the shallow floor that isn't there. Split composite shapes into pieces that really exist.
Question 36 of 36
A concrete loading ramp is a triangular prism. Each triangular side has a horizontal run of 24\text{ ft} and a rise of 2\text{ ft}, and the ramp is 4\text{ ft} wide. Concrete is sold only in whole cubic yards, at \$140 per cubic yard (1\text{ yd}^3 = 27\text{ ft}^3).
How much will the concrete cost?
Hint
Volume in cubic feet → cubic yards → round up to whole cubic yards → multiply by the price.
Concrete comes in whole cubic yards, so buy 4\text{ yd}^3.
Cost: 4 \times \$140 = \$560.
The concrete costs \$560.
Check:4\text{ yd}^3 = 108\text{ ft}^3 \ge 96\text{ ft}^3 ✓, and 3\text{ yd}^3 = 81\text{ ft}^3 would be too little.
Tip: In cost problems with whole units, round up before multiplying by the price. Paying for the exact 96 \div 27 \approx 3.56\text{ yd}^3 gives \$497.78, a price you cannot actually pay.
