Mathematics, 09.04.2020 07:17 connermichaela

Suppose the height of a cylinder is equal to its radius. The cylinder can fit inside a square prism, as shown below.

The cross-sectional areas are still the same and the ratio of the area of the circle to the area of the square is still StartFraction pi Over 4 EndFraction.

StartFraction pi Over 4 EndFraction
Complete the derivation of the formula for a cylinder whose height is equal to its radius.

The prism’s volume is the area of the base,
, times the height, .

Since the ratio of the areas is StartFraction pi Over 4 EndFraction, then the volume of the cylinder is times the volume of the prism.

V = A cylinder inside of a square prism is shown. The cylinder has a height and radius with a length of r. The length of the square prism is 2 r.(4r3), or

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