Question

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.

Answer 1

(i) Whenever we placed a solid right circular cone in a right circular cylinder with full of water,

Then volume of a solid right circular cone is equal to the volume of water failed from the cylinder.

(ii) Total volume of water in a cylinder is equal to the volume of the cylinder.

(iii) Volume of water left in the cylinder = Volume of the right circular cylinder – volume of a right circular cone.

Now, given that

Height of a right circular cone = 120 cm

Radius of a right circular cone = 60 cm

∴ Volume of a right circular cone

= `1/3 pir^2 xx h`

= `1/3 xx 22/7 xx 60 xx 60 xx 120`

= `22/7 xx 20 xx 60 xx 120`

= 144000π cm³

∴ Volume of a right circular cone

= Volume of water falled from the cylinder

= 144000π cm³    ...[From point (i)]

Given that, height of a right circular cylinder = 180 cm

And radius of a right circular cylinder

= Radius of a right circular cone

= 60 cm

∴  Volume of a right circular cylinder

= πr² × h

= π × 60 × 60 × 180

= 648000π cm³

So, volume of a right circular cylinder

= Total volume of water in a cylinder 

= 648000π cm³   ...[From point (ii)]

From point (iii),

Volume of water left in the cylinder

= Total volume of water in a cylinder – Volume of water falled from the cylinder when sold cone is placed in it

= 648000π – 144000π

= 504000π

= `504000 xx 22/7` 

= 1584000 cm³  

= `1584000/(10)^6  m^3`

= 1.584 m³

Hence, the required volume of water left in the cylinder is 1.584 m³.