Back to VolumeSolution key: Inside the box
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Camp · Inside the box
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1 of 8 · volume-c01
A rectangular prism is 5 by 3 by 4. What is the volume?
- Volume of a rectangular box is length times width times height. That is how much fits inside.
- 5 times 3 is 15.
- 15 times 4 is 60.
- The volume is 60.
- Check: 60 ÷ 4 (the height) = 15, and 5 × 3 = 15, so it matches. Volume uses cubic units.
Answer: 60 cu units
2 of 8 · volume-c02
A prism has base area 12 and height 7. What is the volume?
- A prism uses V = base area times height. B is the area of the base, not a side length.
- The base area is already 12, and the height is 7.
- 12 times 7 is 84.
- The volume is 84.
- Check: 84÷7=12, the given base area; volume uses cubic units.
Answer: 84 cu units
3 of 8 · volume-c03
A rectangular pyramid has base 6 by 4 and height 9. What is the volume?
- A pyramid holds one third of a prism with the same base and height. Do not skip the one third.
- The base is 6 × 4 = 24 square units. Multiply by height 9: 24 × 9 = 216 cubic units for a matching prism.
- One third of 216 is 72. Same as (1/3) times 24 times 9.
- The volume is 72.
- Check: Three volumes of 72 total 216, the matching prism volume.
Answer: 72 cu units
4 of 8 · volume-c04
A pyramid has base area 15 and height 6. What is the volume?
- This is a pyramid, so multiply base area times height, then take one third.
- 15 times 6 is 90.
- One third of 90 is 30.
- The volume is 30.
- Check: 30×3=90, the amount before taking one third.
Answer: 30 cu units
5 of 8 · volume-c05
A rectangular prism is 2 by 3 by 6. What is the total surface area?
- Total surface area is the wrapping: every face, front and back.
- The three different face areas are 2 times 3, 2 times 6, and 3 times 6, which are 6, 12, and 18.
- Those add to 36, and the opposite faces double it: 2 times 36 is 72.
- The surface area is 72.
- Check: The six faces total 6+6+12+12+18+18=72 square units.
Answer: 72 sq units
6 of 8 · volume-c06
A cube has edge 4. What is the volume?
- A cube has the same length on every edge.
- Volume is edge times edge times edge.
- 4 times 4 times 4 is 64.
- The volume is 64.
- Check: One 4-by-4 layer is 16; four layers total 64 cubic units.
Answer: 64 cu units
7 of 8 · volume-c07
A cube has edge 5. What is the total surface area?
- A cube has 6 square faces.
- Each face is 5 by 5, so 25.
- 6 times 25 is 150.
- The surface area is 150.
- Check: 150÷6=25, the area of one 5-by-5 face.
Answer: 150 sq units
8 of 8 · volume-c08
A triangular prism has base area 10 and length 8. What is the volume?
- For this triangular prism, multiply the area of a triangular end by the length between the two triangular ends.
- The base area is 10 square units, and the prism length is 8 units: 10 × 8 = 80 cubic units.
- Do not use the one-third. That rule is only for a pyramid.
- The volume is 80.
- Check: 80 ÷ 8 = 10, which matches the triangular base area we were given.
Answer: 80 cu units
Inside the box · Camp
1 of 8 · volume-c01
A rectangular prism is 5 by 3 by 4. What is the volume?
- Volume of a rectangular box is length times width times height. That is how much fits inside.
- 5 times 3 is 15.
- 15 times 4 is 60.
- The volume is 60.
- Check: 60 ÷ 4 (the height) = 15, and 5 × 3 = 15, so it matches. Volume uses cubic units.
Answer: 60 cu units
2 of 8 · volume-c02
A prism has base area 12 and height 7. What is the volume?
- A prism uses V = base area times height. B is the area of the base, not a side length.
- The base area is already 12, and the height is 7.
- 12 times 7 is 84.
- The volume is 84.
- Check: 84÷7=12, the given base area; volume uses cubic units.
Answer: 84 cu units
3 of 8 · volume-c03
A rectangular pyramid has base 6 by 4 and height 9. What is the volume?
- A pyramid holds one third of a prism with the same base and height. Do not skip the one third.
- The base is 6 × 4 = 24 square units. Multiply by height 9: 24 × 9 = 216 cubic units for a matching prism.
- One third of 216 is 72. Same as (1/3) times 24 times 9.
- The volume is 72.
- Check: Three volumes of 72 total 216, the matching prism volume.
Answer: 72 cu units
4 of 8 · volume-c04
A pyramid has base area 15 and height 6. What is the volume?
- This is a pyramid, so multiply base area times height, then take one third.
- 15 times 6 is 90.
- One third of 90 is 30.
- The volume is 30.
- Check: 30×3=90, the amount before taking one third.
Answer: 30 cu units
5 of 8 · volume-c05
A rectangular prism is 2 by 3 by 6. What is the total surface area?
- Total surface area is the wrapping: every face, front and back.
- The three different face areas are 2 times 3, 2 times 6, and 3 times 6, which are 6, 12, and 18.
- Those add to 36, and the opposite faces double it: 2 times 36 is 72.
- The surface area is 72.
- Check: The six faces total 6+6+12+12+18+18=72 square units.
Answer: 72 sq units
6 of 8 · volume-c06
A cube has edge 4. What is the volume?
- A cube has the same length on every edge.
- Volume is edge times edge times edge.
- 4 times 4 times 4 is 64.
- The volume is 64.
- Check: One 4-by-4 layer is 16; four layers total 64 cubic units.
Answer: 64 cu units
7 of 8 · volume-c07
A cube has edge 5. What is the total surface area?
- A cube has 6 square faces.
- Each face is 5 by 5, so 25.
- 6 times 25 is 150.
- The surface area is 150.
- Check: 150÷6=25, the area of one 5-by-5 face.
Answer: 150 sq units
8 of 8 · volume-c08
A triangular prism has base area 10 and length 8. What is the volume?
- For this triangular prism, multiply the area of a triangular end by the length between the two triangular ends.
- The base area is 10 square units, and the prism length is 8 units: 10 × 8 = 80 cubic units.
- Do not use the one-third. That rule is only for a pyramid.
- The volume is 80.
- Check: 80 ÷ 8 = 10, which matches the triangular base area we were given.
Answer: 80 cu units
