How it works
A prism has two identical, parallel bases joined by flat sides. Its volume is
Volume = (area of base) × height
For a rectangular box that is length × width × height; for a cube with edge s it is s³. For a triangular prism, first find the triangle's area, then multiply by the prism's length. The same rule works for cylinders, whose base is a circle: πr²h.
Contest problems often hide one measurement. A cube's surface area is 6s², so a cube with surface area 150 has faces of area 25 and edge 5. Units are cubed: a 2 cm cube has volume 8 cm³, so doubling every edge multiplies the volume by 8.
Prism Volume practice problems with solutions
These problems come from Mathyessy's question bank. Try each one before opening the solution.
A rectangular prism measures 4 by 5 by 6. Find its volume.
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Answer: 120
Volume = 4 × 5 × 6 = 120.
A cube has surface area 150. Find its volume.
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Answer: 125
Each of the 6 faces has area 150 ÷ 6 = 25, so the edge is 5 and the volume is 5³ = 125.
A triangular prism has right triangle bases with legs 9 and 12 and prism length 14. Find its volume.
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Answer: 756
The base is a right triangle with area 9 × 12 ÷ 2 = 54. Volume = 54 × 14 = 756.
A rectangular prism has height 5, width 3 more than the height, and length 4 more than the width. Find its volume.
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Answer: 480
Width = 5 + 3 = 8 and length = 8 + 4 = 12. Volume = 12 × 8 × 5 = 480.
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