A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Given:

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom.

The radius of the cylinder is equal to the radius of the cone.

To do:

We have to find the volume of water left in the cylinder.

Solution:

Height of the right circular cone $h=120\ cm$

Radius of the cone $r=60\ cm$

Height of the right circular cylinder $H=180\ cm$

Radius of the cylinder $R=60\ cm$

Volume of water left in the cylinder $=$ Volume of the cylinder $−$ Volume of the cone

$=\pi r^2 h− \frac{1}{3} \pi r^2 h$

$=\pi (60)^2\times 180- \frac{1}{3} \pi (60)^2 \times 120$

$=\frac{22}{7}\times3600(180-40)$

$=\frac{22}{7}\times3600\times140$

$=1584000\ cm^3$

$=1.584\ m^3$

$=2\ m^3$

The volume of water left in the cylinder is $2\ m^3$.

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Updated on: 10-Oct-2022

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