# 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

**Solution:**

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.

Radius of the cylinder = radius of the cone

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

Volume of cone = (1/3)πr²h

Given, r = 60 cm

h = 120 cm

Volume of cone = (1/3)(22/7)(60)²(120)

= (1/3)(22/7)(3600)(120)

= 452571.429 cm³

Volume of cylinder = πr²h

Given, radius of cone = radius of cylinder = 60 cm

h = 180 cm

Volume = (22/7)(60)²(180)

= (22/7)(3600)(180)

= 2036571.429 cm³

Volume of water left in the cylinder = volume of cylinder - volume of cone

= 2036571.429 - 452571.429

= 1583999.999

= 1584000 cm³

Therefore, the volume of water left in the cylinder is 1584000 cm³.

**✦ Try This: **A solid right circular cone of height 100 cm and radius 40 cm is placed in a right circular cylinder full of water of height 160 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.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 13

**NCERT Exemplar Class 10 Maths Exercise 12.4 Problem 17**

## 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

**Summary:**

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 volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone is 1584000 cm³

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