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Question

A cylinder is having a volume of 231 cu. cm. If the height of the cylinder is 6 cm, then what is the radius of a ball which will fit inside the cylinder?


A

Circle

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B

4 cm

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C

2.5 cm

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D

5 cm

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Solution

The correct options are
A

Circle


C

2.5 cm


Let the radius of the cylinder and ball be rc and rb respectively.

Given, height of the cylinder,h=6 cm

Volume of the cylinder =π×rc2×h=231 cm3

227×rc2×6=231

rc2=231×722×16

rc=3.5 cm

So in order to fit a ball inside the cylinder,

Radius of the ball Radius of the Cylinder

rbrc

rb3.5 cm
So, the ball will fit inside the cylinder if its radius is less than 3.5 cm.
Hence 2.5 cm and 3 cm are the right options.


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