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Q.

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

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Detailed Solution

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

= 23

of the diameter.
Volume of cylinder =Volume of sphere.
Radius of sphere=4cm.
We need to find radius of the base of the cylinder.
We know that,
Volume of the sphere

= 43 π r 3

.
Volume of the cylinder

= π r 2 h

.
Let the radius of the cylinder

= r

.
Height of the cylinder

= 23

of the diameter

H e i g h t = 23 × 2 r H e i g h t = 4 r 3

As the volume of sphere = volume of cylinder.
Let’s put the values in their formulas,

43 π r 3 = π r 2 4 r 3 43 π 4 × 4 × 4 = 43 π r 3 43 = r 3 4 = r

So, the radius of the cylinder = 4 cm.
Therefore, the final answer is 4.

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