# A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass

**Solution:**

A figure is drawn to visualize the shape.

As mentioned that the glass is in the shape of a frustum of a cone

Therefore, the capacity of the glass = Volume of the frustum of the cone.

Let us find the capacity of the glass by using formulae

Volume of a frustum of a cone = 1/3 πh(r_{1}^{2} + r_{2}^{2} + r_{1}r_{2}), where r_{1}, r_{2}, and h are the radii and height of the frustum of the cone respectively.

Height of glass, h = 14 m

Radius of the larger base, r_{1} = 4 cm / 2 = 2 cm

Radius of the smaller base, r_{2} = 2 cm / 2 = 1 cm

The capacity of the glass = Volume of frustum of a cone = 1/3 πh(r_{1}^{2} + r_{2}^{2} + r_{1}r_{2})

= 1/3 × 22/7 × 14 cm × (2 cm)^{2} + (1 cm)^{2} + 2 cm × 1 cm

= 44/3 cm × (4 cm^{2} + 1 cm^{2} + 2 cm^{2})

= 44/3 cm × 7cm^{2}

= 308/3 cm^{2}

= 102 ⅔ cm^{2}

Therefore, the capacity of the glass is 102 ⅔ cm^{3}.

**Video Solution:**

## A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.4 Question 1 :

A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameters of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass

The capacity of the frustum of a cone shaped drinking glass of height 14 cm having diameters of its circular ends as 4 cm and 2 cm is 102 ⅔ cm^{3}