Cylinder – Volume
A cylinder’s volume is its circular base area times its height: V = π × r² × h.
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A cylinder is a 3D solid with two circular ends and a curved side, like a can or a water tank. Volume answers “how much does it hold?” and is measured in cubic units. The formula is V = π × r² × h, where r is the radius of the circular base and h is the height. Use π ≈ 3.14 unless told otherwise.
The formula works by finding the area of the circular base (π × r²) and multiplying by the height to stack that area through the solid. Always square the radius first, then multiply by π, then by the height.
If a problem gives the diameter of the base instead of the radius, divide by 2 to get r before using the formula. Keep volume (cubic units) separate from surface area (square units).
Worked example
A cylindrical tank has radius 4 ft and height 10 ft. How many cubic feet does it hold? (π ≈ 3.14)
- “How many cubic feet does it hold” means volume.
- Write the formula: V = π × r² × h = 3.14 × 4² × 10.
- Square the radius first: 4² = 16.
- Multiply: 3.14 × 16 × 10 = 502.4.
502.4 cubic feet
On the test: Volume is measured in cubic units; “how much does it hold” signals volume rather than surface area.
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