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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