Volume of a rectangular prism: V = Bh, where B is the area of the base.
Step-by-step solution
Area of the base (the 8 \times 5 bottom): B = 8 \times 5 = 40\text{ in}^2.
Multiply by the height: V = Bh = 40 \times 3 = 120.
Volume is measured in cubic units, so the volume is 120\text{ in}^3.
Check:120 \div (8 \times 5) = 120 \div 40 = 3, which is the height ✓.
Tip: Volume always multiplies all three dimensions. If you see an answer that adds them, or one that is much bigger because it counts faces, it is a trap.
Question 2 of 36
Fill in
A closed gift box has the dimensions shown.
How many square inches of wrapping paper are needed to cover the box exactly, with no overlap?
\text{in}^2
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Wrapping paper covers all 6 faces. Use SA = ph + 2B (formula sheet), where p is the perimeter of the base.
Step-by-step solution
Base (bottom) is 10 \times 6: B = 60\text{ in}^2.
Perimeter of the base: p = 2(10) + 2(6) = 32\text{ in}.
Lateral area (the 4 sides): ph = 32 \times 4 = 128\text{ in}^2.
Top and bottom: 2B = 2 \times 60 = 120\text{ in}^2.
Tip: If you got 124, you counted each face once. Every face of a box has a matching twin, so the total is always doubled.
Question 3 of 36
A storage cube has edges that are each 5\text{ cm} long.
What is the volume of the cube?
Hint
A cube is a box whose length, width and height are all the same. Multiply all three.
Step-by-step solution
For any box, V = lwh. In a cube, l = w = h = 5.
V = 5 \times 5 \times 5.
5 \times 5 = 25, and 25 \times 5 = 125.
The volume is 125\text{ cm}^3.
Check: a 5 \times 5 bottom layer holds 25 unit cubes, and there are 5 layers: 25 \times 5 = 125 ✓.
Tip:5^3 means 5 \times 5 \times 5, not 5 \times 3. For a cube, V = s^3. On the calculator use the ^ key: 5^3enter.
Question 4 of 36
A cereal box has the dimensions shown.
How much cereal can the box hold?
Hint
The amount a box holds is its volume. Find the area of the base, then multiply by the height.
Step-by-step solution
Use V = Bh for a rectangular prism. Take the bottom of the box as the base: it is 7\text{ in} by 2\text{ in}.
Area of the base: B = 7 \times 2 = 14\text{ in}^2.
Multiply by the height: V = 14 \times 10 = 140.
The box holds 140\text{ in}^3 of cereal.
Check: any order of multiplying gives the same volume: 7 \times 10 = 70 and 70 \times 2 = 140 ✓.
Tip: "How much can it hold" is always a volume question, and volume is measured in cubic units. An answer in square inches, or one made by adding, cannot be right.
Question 5 of 36
Fill in
A closed jewelry box is a rectangular prism 9\text{ cm} long, 5\text{ cm} wide and 4\text{ cm} tall. Dana wants to cover the whole outside of the box with fabric, with no overlap.
How many square centimeters of fabric does she need?
\text{cm}^2
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Covering the outside means all 6 faces. Use SA = ph + 2B, or add the three different face areas and double the total.
Step-by-step solution
Base (bottom): B = 9 \times 5 = 45\text{ cm}^2.
Perimeter of the base: p = 2(9) + 2(5) = 28\text{ cm}.
Lateral area (the 4 sides): ph = 28 \times 4 = 112\text{ cm}^2.
Top and bottom: 2B = 2 \times 45 = 90\text{ cm}^2.
Tip: A box has three pairs of matching faces. If your total is 101, you counted each face only once — double it.
Question 6 of 36
A child's wooden building block is a cube with edges 4\text{ in} long. A parent wants to paint every face of the block.
How many square inches will be painted?
Hint
A cube has 6 faces, and every face is a square with the same side length.
Step-by-step solution
Each face is a square 4\text{ in} by 4\text{ in}: area = 4^2 = 16\text{ in}^2.
A cube has 6 identical faces.
Surface area: SA = 6 \times 16 = 96.
The parent will paint 96\text{ in}^2.
Check: using the formula sheet, SA = ph + 2B with p = 16, h = 4, B = 16: 64 + 32 = 96 ✓.
Tip: For a cube, memorize two quick facts: volume = s^3 and surface area = 6s^2. Paint, wrapping and fabric questions want the surface area; "holds" or "fills" questions want the volume.
Question 7 of 36
A self-storage unit is shaped like a rectangular prism. Its floor is 12\text{ ft} by 10\text{ ft}, and it holds 960\text{ ft}^3.
What is the height h of the unit?
Hint
Write V = lwh, substitute the three numbers you know, and solve for h.
Step-by-step solution
Formula: V = lwh.
Substitute: 960 = 12 \times 10 \times h.
Floor area: 12 \times 10 = 120, so 960 = 120h.
Divide both sides by 120: h = 960 \div 120 = 8.
The unit is 8\text{ ft} high.
Check:12 \times 10 \times 8 = 960 ✓.
Tip: To find a missing dimension from the volume, divide the volume by the product of the other two dimensions. You can also test each answer choice in 12 \times 10 \times h.
Question 8 of 36
Fill in
Rosa is filling the raised garden bed shown with soil to a depth of 1.5\text{ ft}.
Garden soil is sold in bags that each hold 2\text{ ft}^3. How many bags does Rosa need?
bags
Type your answer in the box. Fractions like 3/4 are fine.
Hint
First find the volume of soil in cubic feet, then figure out how many 2\text{ ft}^3 bags make that much.
Step-by-step solution
The soil forms a box 8\text{ ft} by 4\text{ ft} by 1.5\text{ ft}.
Check:24 \text{ bags} \times 2\text{ ft}^3 = 48\text{ ft}^3, and 48 \div (8 \times 4) = 1.5\text{ ft} deep ✓.
Tip: Decimals do not change the method. Multiply length × width × depth, then divide by the size of one bag. If the division is not a whole number, round up because you cannot buy part of a bag.
Question 9 of 36
Drop-down
A company ships products in the box shown.
Select the correct value for each blank.
The box holds of packing material, and it takes of cardboard to make the closed box (ignore overlaps).
Choose an answer from each menu.
Hint
"Holds" means volume (V = Bh). "Cardboard to make the box" means surface area (SA = ph + 2B).
Step-by-step solution
Volume
B = 12 \times 9 = 108\text{ in}^2.
V = Bh = 108 \times 4 = 432\text{ in}^3.
Surface area
Perimeter of the base: p = 2(12) + 2(9) = 42\text{ in}.
Tip: Look at the units in the choices: cubic inches can only be a volume, square inches can only be an area.
Question 10 of 36
A toy company makes a box that is 3\text{ in} by 4\text{ in} by 5\text{ in}. A new, larger model doubles each of the three dimensions.
The volume of the new box is how many times the volume of the original box?
Hint
Find both volumes and compare them, or think about what happens to l \times w \times h when each factor is multiplied by 2.
Step-by-step solution
Original volume: V = 3 \times 4 \times 5 = 60\text{ in}^3.
New dimensions: 6\text{ in}, 8\text{ in}, 10\text{ in}.
New volume: V = 6 \times 8 \times 10 = 480\text{ in}^3.
Compare: 480 \div 60 = 8.
The new volume is 8 times the original.
Check: each dimension is multiplied by 2, so the volume is multiplied by 2 \times 2 \times 2 = 2^3 = 8 ✓.
Tip: When every length of a solid is multiplied by k, the surface area is multiplied by k^2 and the volume by k^3. Doubling does not double the volume.
Question 11 of 36
Select all
Use the rectangular prism shown.
Select all statements that are true.
Select all that apply.
Hint
Work out B, p, V = Bh, the lateral area ph, and SA = ph + 2B, then compare each statement.
Step-by-step solution
Take the 10 \times 4 face as the base and 3\text{ ft} as the height.
B = 10 \times 4 = 40\text{ ft}^2; p = 2(10) + 2(4) = 28\text{ ft}.
Volume: V = Bh = 40 \times 3 = 120\text{ ft}^3. A is true.
Lateral area (4 sides): ph = 28 \times 3 = 84\text{ ft}^2. C is true.
Surface area: SA = ph + 2B = 84 + 80 = 164\text{ ft}^2. B is true.
D (82) is half of the surface area, and E (17) adds the edges — both false.
Tip: To work backwards from a volume, divide by the area of the base, not by just one side. Dividing 3{,}168 by 24 alone gives 132, which is far too deep for a fish tank — always ask if the answer is sensible.
Question 14 of 36
A rectangular sandbox is 6\text{ ft} long and 5\text{ ft} wide. Jamal wants to fill it with sand to a depth of 1.2\text{ ft}. Play sand is sold in bags that each hold 0.5\text{ ft}^3.
How many bags of sand does Jamal need?
Hint
First find the volume of sand (length × width × depth). Then figure out how many half-cubic-foot bags make that volume.
Step-by-step solution
Volume of sand: V = 6 \times 5 \times 1.2.
6 \times 5 = 30\text{ ft}^2 (the floor of the sandbox), and 30 \times 1.2 = 36\text{ ft}^3.
Each bag holds 0.5\text{ ft}^3, so divide: 36 \div 0.5 = 72.
Jamal needs 72 bags.
Check:72 bags \times\ 0.5\text{ ft}^3 = 36\text{ ft}^3, which matches the volume ✓.
Tip: Dividing by a number less than 1 makes the answer bigger. Since each bag is only half a cubic foot, you need twice as many bags as cubic feet. If your answer is smaller than 36, you multiplied instead of dividing.
Question 15 of 36
Drop-down
A moving company sells a box that is 18\text{ in} long, 18\text{ in} wide and 16\text{ in} tall. A customer wants to know how much the box can hold.
Select the correct choice for each blank.
To answer the customer, find the box's . The box can hold .
Choose an answer from each menu.
Hint
Ask yourself: is the customer asking about the space inside, or the material on the outside? Then look at the units.
Step-by-step solution
"How much the box can hold" is the space inside, so we need the volume.
Check:5{,}184 \div 324 = 16, the height ✓. For comparison, the surface area is 2(324) + 2(18 \cdot 16) + 2(18 \cdot 16) = 648 + 576 + 576 = 1{,}800\text{ in}^2 — a different number with different units.
Tip: Volume answers are in cubic units (\text{in}^3); surface area answers are in square units (\text{in}^2). Matching the units to the question removes many wrong choices at once.
Question 16 of 36
A warehouse uses cube-shaped shipping crates. A new crate has edges that are 3 times as long as the edges of the old crate.
The surface area of the new crate is how many times the surface area of the old crate?
Hint
Try it with numbers: give the old crate an edge of 1 and the new crate an edge of 3, then compare 6s^2 for each.
Step-by-step solution
Let the old edge be s. Old surface area: 6s^2.
New edge: 3s. New surface area: 6(3s)^2 = 6 \cdot 9s^2 = 54s^2.
Compare: 54s^2 \div 6s^2 = 9.
The new crate has 9 times the surface area.
Check: with numbers, old edge 1: SA = 6. New edge 3: SA = 6 \times 9 = 54. 54 \div 6 = 9 ✓.
Tip: When every length is multiplied by k, areas are multiplied by k^2 and volumes by k^3. Here k = 3: area \times 9, volume \times 27.
Question 17 of 36
Drag and drop
Drag each closed box into the column that shows its surface area. One box will not be used.
SA = 52 square units
SA = 88 square units
SA = 94 square units
Tap a tile, then tap a box to place it.
Hint
For each box, find the three different face areas, add them, and double the sum. Watch out for a box whose volume matches a column.
2 \times 4 \times 11: 2(8 + 22 + 44) = 2(74) = 148 → not used. Its volume is 2 \times 4 \times 11 = 88, which is the trap.
Check: the 2 \times 2 \times 10 box with SA = ph + 2B: p = 8, h = 10, B = 4: 80 + 8 = 88 ✓.
Tip: Read the column headings carefully. A column labeled "surface area" needs square units; a matching volume number is a deliberate trap.
Question 18 of 36
A gift box is a cube. Exactly 294\text{ in}^2 of paper covers all six faces with no overlap.
How long is each edge of the box?
Hint
The surface area of a cube is 6s^2. Undo the 6 first, then undo the square.
Step-by-step solution
Set up the equation: 6s^2 = 294.
Divide by 6: s^2 = 294 \div 6 = 49. This is the area of one face.
Take the square root: s = \sqrt{49} = 7.
Each edge is 7\text{ in} long.
Check:6 \times 7^2 = 6 \times 49 = 294 ✓.
Tip: Working backwards reverses the order of operations: the formula squares and then multiplies by 6, so you divide by 6 and then take the square root. On the TI-30XS, use 2ndx² for \sqrt{\ }.
Question 19 of 36
Fill in
A metal planter box has no top, as shown.
How many square inches of sheet metal are needed to make the planter (the bottom and the four sides)?
\text{in}^2
Type your answer in the box. Fractions like 3/4 are fine.
Hint
List the faces that really exist: one bottom, two long sides, two short sides. There is no lid.
Step-by-step solution
Bottom: 30 \times 12 = 360\text{ in}^2 (only one, because there is no top).
Two long sides: 2(30 \times 10) = 2(300) = 600\text{ in}^2.
Two short sides: 2(12 \times 10) = 2(120) = 240\text{ in}^2.
Total: 360 + 600 + 240 = 1{,}200.
The planter needs 1{,}200\text{ in}^2 of metal.
Check: the full closed box would be SA = ph + 2B = (84)(10) + 2(360) = 840 + 720 = 1{,}560. Remove the missing top: 1{,}560 - 360 = 1{,}200 ✓.
Tip: For open boxes, use ph + B instead of ph + 2B. Always picture the real object and count only the faces it has.
Question 20 of 36
A contractor is pouring a concrete patio slab that is 12\text{ ft} long, 9\text{ ft} wide and 6inches thick. Concrete is ordered in cubic yards (1\text{ yd}^3 = 27\text{ ft}^3).
How many cubic yards of concrete are needed?
Hint
Make all three measurements feet before multiplying. Then change cubic feet to cubic yards.
Check: in yards the slab is 4\text{ yd} \times 3\text{ yd} \times \tfrac{1}{6}\text{ yd}, and 4 \times 3 \times \tfrac{1}{6} = 2 ✓.
Tip:1\text{ yd} = 3\text{ ft}, but 1\text{ yd}^3 = 3 \times 3 \times 3 = 27\text{ ft}^3. Divide cubic feet by 27, not by 3.
Question 21 of 36
A craft box is 10\text{ in} long, 6\text{ in} wide and 4\text{ in} tall. Mia packs it with wooden cubes that are 2\text{ in} on each edge, with no gaps.
How many cubes fit in the box?
Hint
Count how many cubes fit along the length, along the width, and along the height. Then multiply.
Step-by-step solution
Along the length: 10 \div 2 = 5 cubes.
Along the width: 6 \div 2 = 3 cubes.
Along the height: 4 \div 2 = 2 layers.
Total: 5 \times 3 \times 2 = 30.
30 cubes fit in the box.
Check: box volume = 10 \times 6 \times 4 = 240\text{ in}^3; one cube = 2^3 = 8\text{ in}^3; 240 \div 8 = 30 ✓. (Dividing volumes works here only because every edge divides evenly.)
Tip: A small cube's volume is s^3, not s. Dividing the box volume by 2 instead of by 2^3 = 8 makes the count four times too big.
Question 22 of 36
A bar of soap is shaped like a rectangular prism 3.5\text{ in} long, 2.4\text{ in} wide and 1.25\text{ in} thick.
What is the volume of the bar of soap?
Hint
Multiply all three dimensions. A calculator helps with the decimals.
Step-by-step solution
Base: B = 3.5 \times 2.4 = 8.4\text{ in}^2.
Multiply by the thickness: V = 8.4 \times 1.25 = 10.5.
The volume is 10.5\text{ in}^3.
Check: estimate with rounded numbers: 3.5 \times 2.4 \approx 8, and 8 \times 1.25 = 10. The exact answer 10.5 is close ✓.
Tip: Decimal dimensions follow exactly the same rule: V = lwh. Estimate first so you can spot a decimal-point slip, such as 1.05 or 105.
Question 23 of 36
Kayla is covering the closed toolbox shown with waterproof vinyl on every face.
How much vinyl does she need, with no overlap?
Hint
Every face gets covered, so find the total surface area: SA = ph + 2B.
Step-by-step solution
Base: B = 20 \times 8 = 160\text{ in}^2.
Perimeter of the base: p = 2(20) + 2(8) = 56\text{ in}.
Tip: When two dimensions are known, multiply them first and divide the volume by that product. The answer does not have to be a whole number — a width of 2.5\text{ ft} is perfectly normal.
Question 25 of 36
The swimming pool shown is filled completely with water from a hose.
One cubic foot holds about 7.5 gallons of water, and the hose delivers 12 gallons per minute. About how many hours will it take to fill the pool?
Hint
Three steps: volume in cubic feet → gallons → minutes. Then change minutes to hours.
Tip: In multi-step unit problems, write the unit after every number. If the units do not end up as the unit the question asks for (here, hours), a step is missing.
Question 26 of 36
Fill in
A closed box has a square base that measures 6\text{ in} on each side. The total surface area of the box is 192\text{ in}^2.
What is the height h of the box, in inches?
h = in
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Use SA = ph + 2B from the formula sheet. Find B and p for the square base, substitute, and solve for h.
Step-by-step solution
Base area: B = 6 \times 6 = 36\text{ in}^2, so 2B = 72\text{ in}^2.
Perimeter of the base: p = 4 \times 6 = 24\text{ in}.
Tip: Working backwards from surface area: first subtract the two bases, then divide what is left by the perimeter. A common slip is dividing 192 by 24 before subtracting (which gives 8).
Question 27 of 36
Fill in
A cube-shaped storage ottoman holds 512\text{ in}^3 inside.
How long is each inside edge of the ottoman, in inches?
in
Type your answer in the box. Fractions like 3/4 are fine.
Hint
For a cube, V = s^3. Find the number that, used as a factor three times, gives 512.
Check:8 \times 8 = 64 for the bottom layer, and 8 layers make 64 \times 8 = 512\text{ in}^3 ✓.
Tip: On the TI-30XS, find a cube root with 32nd^ (ⁿ√) 512enter. Without a calculator, try whole numbers: 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125, 6^3 = 216, 7^3 = 343, 8^3 = 512. Dividing 512 by 3 is a common mistake.
Question 28 of 36
Select all
A jewelry box is 4\text{ in} long, 3\text{ in} wide and 2\text{ in} tall. A larger box is made by doubling each dimension.
Select all statements that are true.
Select all that apply.
Hint
Compute the volume and surface area of both boxes, or use the rule: lengths \times k, areas \times k^2, volumes \times k^3.
V = 8 \times 6 \times 4 = 192\text{ in}^3. A is true.
192 \div 24 = 8 = 2^3, so the volume is 8 times as large. B is true.
SA = 2(48 + 32 + 24) = 2(104) = 208\text{ in}^2, and 208 \div 52 = 4 = 2^2. C is true.
D says 104\text{ in}^2 — that only doubles the area. False.
E says 48\text{ in}^3 — that only doubles the volume. False.
The true statements are A, B and C.
Check: with the rule k = 2: 24 \times 8 = 192 ✓ and 52 \times 4 = 208 ✓.
Tip: Doubling every dimension never simply doubles the volume or the area. Volume uses three dimensions (2 \times 2 \times 2), area uses two (2 \times 2).
Question 29 of 36
A family is choosing a storage bin. The four bins below have the inside dimensions shown (in feet).
Bin
Length
Width
Height
A
10
10
2
B
8
5
6
C
6
6
6
D
12
4
4
Which bin holds the most?
Hint
Don't judge by the longest side. Compute l \times w \times h for every bin and compare.
Step-by-step solution
Compute each volume with V = lwh:
Bin A: 10 \times 10 \times 2 = 200\text{ ft}^3.
Bin B: 8 \times 5 \times 6 = 240\text{ ft}^3.
Bin C: 6 \times 6 \times 6 = 216\text{ ft}^3.
Bin D: 12 \times 4 \times 4 = 192\text{ ft}^3.
The largest volume is 240\text{ ft}^3, so Bin B holds the most.
Check: order the volumes: 192 < 200 < 216 < 240 — B is at the top ✓.
Tip: The bin with the longest side (D) actually holds the least. Shapes can fool the eye; always calculate.
Question 30 of 36
Fill in
A closed shipping box is 10\text{ cm} long and 4\text{ cm} wide. Its total surface area is 220\text{ cm}^2.
What is the height of the box, in centimeters?
h = cm
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Use SA = ph + 2B. Find p and B from the length and width, then solve for h.
Step-by-step solution
Base: B = 10 \times 4 = 40\text{ cm}^2, so 2B = 80\text{ cm}^2.
Perimeter of the base: p = 2(10) + 2(4) = 28\text{ cm}.
Tip: Undo the steps in reverse: first remove the top and bottom (2B), then divide what is left (the four sides) by the perimeter. Forgetting to subtract 2B gives 220 \div 28 \approx 7.9, which does not check.
Question 31 of 36
Luis will paint the four outside walls of a shed. The shed's floor is 10\text{ ft} by 8\text{ ft}, and the walls are 7\text{ ft} high. He will not paint the roof or the floor, and he will not paint the door, which is 3\text{ ft} wide and 7\text{ ft} high.
One quart of paint covers 80\text{ ft}^2, and paint is sold only in whole quarts. How many quarts must Luis buy?
Hint
Find the area of the four walls (ph), subtract the door, then divide by the coverage. Can he buy part of a quart?
Step-by-step solution
Perimeter of the floor: p = 2(10) + 2(8) = 36\text{ ft}.
Area of the four walls: ph = 36 \times 7 = 252\text{ ft}^2.
Subtract the door: 3 \times 7 = 21\text{ ft}^2, so 252 - 21 = 231\text{ ft}^2.
Quarts needed: 231 \div 80 = 2.8875.
He cannot buy part of a quart, and 2 quarts would cover only 160\text{ ft}^2. Round up to 3.
Tip: When you buy supplies, always round up — running short is not an option. Also remove openings like doors and windows only when the problem tells you to.
Question 32 of 36
Fill in
A plastic storage bin measures 36\text{ in} long, 24\text{ in} wide and 18\text{ in} tall.
What is the volume of the bin in cubic feet? (1\text{ ft}^3 = 1{,}728\text{ in}^3)
\text{ft}^3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Either change each measurement to feet first, or find the volume in cubic inches and divide by 1{,}728.
Tip:1\text{ ft} = 12\text{ in}, so 1\text{ ft}^3 = 12 \times 12 \times 12 = 1{,}728\text{ in}^3. Dividing 15{,}552 by 12 gives 1{,}296 — a huge, wrong answer. Converting each length first is usually easier.
Question 33 of 36
Marcus will paint the four walls and the ceiling of the room shown. He will not paint the floor. Ignore doors and windows.
One gallon of paint covers 350\text{ ft}^2. Paint is sold only in whole gallons. How many gallons must Marcus buy for one coat?
Hint
Walls = the lateral area ph. Ceiling = one base B. Add them, divide by 350, and think about how to round.
Step-by-step solution
Perimeter of the floor: p = 2(14) + 2(12) = 52\text{ ft}.
Tip: Not every problem uses the full SA = ph + 2B. Decide which faces are really being covered, and when buying supplies, always round up.
Question 34 of 36
The cargo area of a moving truck is a rectangular prism 20\text{ ft} long, 8\text{ ft} wide and 7\text{ ft} tall. The movers load boxes that are each 2\text{ ft} long, 2\text{ ft} wide and 1.5\text{ ft} tall. All boxes stand upright in the same direction, and boxes cannot be cut.
What is the greatest number of boxes that fit in the truck?
Hint
Count whole boxes along each direction. A row or layer that only partly fits does not count.
Step-by-step solution
Along the length: 20 \div 2 = 10 boxes.
Along the width: 8 \div 2 = 4 boxes.
Along the height: 7 \div 1.5 = 4.67, so only 4 whole layers fit (a 5th layer would need 7.5\text{ ft}).
Total: 10 \times 4 \times 4 = 160.
At most 160 boxes fit.
Check: the 4 layers use 4 \times 1.5 = 6\text{ ft} of the 7\text{ ft} height, leaving a 1\text{ ft} gap that no box fits into ✓.
Tip: Dividing volumes (1{,}120 \div 6 \approx 186) pretends boxes can be squeezed into the leftover gap. When objects are solid, count along each edge and round each count down.
Question 35 of 36
Ana is spreading topsoil over a garden bed 20\text{ ft} long and 9\text{ ft} wide, to a depth of 4inches. Topsoil is sold only in whole cubic yards, at \$35 per cubic yard (1\text{ yd}^3 = 27\text{ ft}^3).
How much will Ana spend on topsoil?
Hint
Change the depth to feet, find the volume in cubic feet, convert to cubic yards, then decide how many whole cubic yards she must buy.
Step-by-step solution
Depth in feet: 4\text{ in} = \tfrac{4}{12} = \tfrac{1}{3}\text{ ft}.
Tip: Multi-step supply problems hide three traps: mixed units (inches vs feet), cubic conversions (27, not 3), and rounding up to whole units before you multiply by the price.
Question 36 of 36
A wooden crate is 3\text{ ft} long, 2\text{ ft} wide and 2\text{ ft} tall. It is packed full, with no gaps, of cube-shaped boxes that are 6inches on each edge.
How many small boxes fit in the crate?
Hint
Use the same unit for everything. How many 6-inch boxes fit along a 1-foot length?
Step-by-step solution
6\text{ in} = 0.5\text{ ft}, so 2 small boxes fit in every foot.
Tip: In a packing problem, convert to one unit first, then count along each edge. Dividing the crate volume (12\text{ ft}^3) by an edge (0.5) or by a face area (0.25) instead of the box volume (0.125\text{ ft}^3) gives a wrong count.
