The volume and the height of a cylinder are equal to the volume and height of the frustum of a square pyramid whose upper side is 3 meters and the lower side is 8 meters. Compute the radius of the base of the cylinder.

 

r = ______ meters
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The frustum is the difference in volume of two pyramids. We need their heights and base areas.

The base areas are 64sq m and 9sq m. To find the height of the smaller pyramid we use similar triangles. The ratio of the heights is the ratio of the side lengths=3/8. So, if h is the height of the larger pyramid, the height of the smaller one is 3h/8. The height of the frustum is h-3h/8=5h/8=height of cylinder.

The volume of a pyramid is ⅓AH where A is the base area and H the height.

Volume of the cylinder is AH, where A=πr² and H=5h/8. Volume=5hπr²/8=volume of frustum.

Volume of frustum=⅓(64h-9×3h/8)=485h/24=5hπr²/8, 97h/3=hπr²,

r²=97/(3π)=10.292, r=3.208m approx.

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