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Question

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?

(a) x22π

(b) x2π

(c) 2xπ

(d) π2x

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Solution

Let V1 be the volume of the cylinder with radius r and height h, then

……. (1)

Now, let V2 be the volume of the box, then

It is given that V1 =1/4 V2Therefpre,

Hence, the correct option is (b)


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