a rectangle with height $6$ and length $4$ is wrapped around a cylinder with height $6$. the rectangle perfectly covers the curved surface of the cylinder without overlap. what is the volume of the cylinder?

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31-10-2022
Mathematics

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a rectangle with height $6$ and length $4$ is wrapped around a cylinder with height $6$. the rectangle perfectly covers the curved surface of the cylinder without overlap. what is the volume of the cylinder?

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jcmacahia7 jcmacahia7 · Answer 1 · 2022-11-02T08:56:40-04:00

The volume of the cylinder is 7.64 units.

If the rectangle and the cylinder has the same height, and it perfectly covers the curved surface of the cylinder without overlap, then the circumference of the base of the cylinder is equal to the length of the rectangle.

length of rectangle = circumference of the base of the cylinder = 4

Solve for the radius of the base of the cylinder using the formula for the circumference of a circle.

C = 2πr

4 = 2πr

r = 0.6366197724

Solve for the volume of the cylinder given that the height is 6 and the radius of the base is 0.6366197724.

V = πr²h

V = π(0.6366197724)²(6)

V = 7.639437268

V = 7.64

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