# A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π

**Solution:**

The visualisation of the solid figure is drawn below.

As the solid is made up of a conical part and a hemispherical part. The volume of a solid is the space occupied inside it or the capacity that an object holds.

Volume of the solid = volume of the conical part + volume of the hemispherical part

Let us find the volume of the solid by using formulae;

Volume of the hemisphere = 2/3 πr^{3}

where r is the radius of the hemisphere

Volume of the cone = 1/3 πr^{2}h

where r and h are the radius and height of the cone respectively.

Radius of hemispherical part = Radius of conical part = r = 1 cm

Height of conical part = h = r = 1 cm

Volume of the solid = volume of the conical part + volume of the hemispherical part

= 1/3 πr^{2}h + 2/3 πr^{3}

= 1/3 πr^{3} + 2/3 πr^{3}

= πr^{3}

= π (1cm)^{3}

= π cm^{3}

Thus, the volume of the solid is π cm^{3}.

**Video Solution:**

## A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π

### NCERT Solutions Class 10 Maths - Chapter 13 Exercise 13.2 Question 1 :

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π

The volume of a solid of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone being equal to its radius is π cm^{3}.