Question

A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.

Answer 1

Radius of base of cylinder is 4 cm

Solution:

Find volume of sphere

sphere of radius 4 cm

$Volume\ of\ sphere = \frac{4}{3} \pi r^3$

$Volume\ of\ sphere = \frac{4}{3} \times \pi \times 4^3 --------- eqn\ 1$

The volume of cylinder is given as:

$Volume \:of \:a \:cylinder = \pi r^{2}h$

Where,

r is radius

h is height

A cylinder whose height is two thirds of its diameter

$h = \frac{2}{3} \times diameter\\\\h = \frac{2}{3} \times 2r\\\\h = \frac{4r}{3}$

Therefore,

$volume\ of\ cylinder = \pi \times r^2 \times \frac{4r}{3} ---- eqn\ 2$

According to question,

volume of the cylinder = volume of the sphere

$\frac{4}{3} \times \pi \times 4^3 = \pi \times r^2 \times \frac{4r}{3}\\\\4^3 = r^3\\\\r = 4$

Thus radius of base of cylinder is 4 cm

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