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Volume of prisms & cylinders

Measurement

Japanese school year: Elementary 6

What you learn

Learn how to calculate the volumes of prisms and cylinders by multiplying base area by height. This technique is applied when determining container capacities, storage tanks, and architectural columns. Prior mastery of calculating base areas, such as triangles and circles, along with rectangular prism volumes will ensure solid comprehension.

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Key points

This formula finds the volume V of a prism or cylinder. Multiply the base area S by height h.

V=ShV = Sh

This formula finds the volume V of a cylinder. Multiply the circular base area πr² by height h.

V=πr2hV = \pi r^2 h

This formula finds the side surface area SsideS_{\text{side}} of a cylinder. Multiply the base circumference 2πr2\pi r by height hh.

Sside=2πrhS_{\mathrm{side}} = 2\pi rh

This formula finds the total surface area S of a cylinder. Add the two base areas 2πr² and the side area 2πrh.

S=2πr2+2πrhS = 2\pi r^2 + 2\pi rh

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