Multiple choice

A sphere and a cone have equal radii and equal volume. Find the relation between radius and height of the cone.

  1. h = 2r

  2. h = 4r

  3. h = 3r

  4. h = r
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B Correct answer
Explanation

Volume of sphere is (4/3)pi*r^3 and volume of cone is (1/3)pi*r^2*h. Setting them equal: (4/3)pi*r^3 = (1/3)pi*r^2*h. Dividing both sides by (1/3)pi*r^2 gives 4r = h.

AI explanation

Equating the volume of the sphere, 4/3 times pi times r cubed, to the volume of the cone, 1/3 times pi times r squared times h, we can cancel pi, one third, and r squared from both sides. This leaves the relation 4r = h. Therefore, the height of the cone is equal to 4r.

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