Prisms & cylinders

Japanese school year: Elementary 5

What you learn

Explore the structures and properties of prisms and cylinders, examining relationships between bases and lateral surfaces alongside their nets. Understanding these solid shapes is crucial for calculating surface area and volume in real-world contexts. Reviewing cuboids, rectangles, and circle properties beforehand will help you understand the concepts smoothly.

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Key points

This fundamental formula calculates the volume $V$ of a prism or cylinder. It is obtained by multiplying the base area $S$ by the height $h$ .

V = Sh

This formula calculates the volume $V$ of a cylinder. Given the base radius $r$ and the height $h$ , multiply the circular base area $\pi r^2$ by the height $h$ .

V = \pi r^2 h

This formula finds the width $\ell$ of the lateral rectangle in a cylinder's net. The width matches the perimeter of the circular base with radius $r$ , which is $2\pi r$ .

\ell = 2\pi r

This formula calculates the total surface area $S$ of a cylinder. Add the areas of the two circular bases ( $2\pi r^2$ ) and the lateral area ( $2\pi rh$ ), with base radius $r$ and height $h$ .

S = 2\pi r^2 + 2\pi rh

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Practice 1Coming soon