Question 86
The radius of a sphere is 3 times the radius of a cylinder. If their volumes are equal, find the height of the cylinder.
Solution
radius of sphere = 3 radius of cyclinder
let R be the radius of sphere
and r be the the radius of cyclinder
R = 3r
vol of sphere =vol of cyclinder
$$\frac{4}{3}\pi \times R^3 = \pi \times r^2\times h$$
$$\frac{4}{3}\pi \times (3r)^3 = \pi \times r^2\times h$$
h = 36r
h =36 times its radius
6
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