# The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases

**Solution:**

The radius of the spherical balloon before and after filling air has radii of 7 cm and 14 cm respectively as shown below.

The surface area of a sphere = 4πr^{2}

The radius of the balloon before pumping air, r₁ = 7cm

The radius of the balloon after pumping air, r₂ = 14cm

The surface area of the balloon before pumping air, SA₁ = 4π(r₁)^{2}

The surface area of the balloon after pumping air, SA₂ = 4π(r₂)^{2}

The ratio of the surface areas of the balloon,

= SA₁/CSA₂

= 4π(r₁)^{2}/4π(r₂)^{2}

= (r₁)^{2}/(r₂)^{2}

= (r₁/r₂)^{2}

= (7/14)^{2}

= (1/2)^{2}

= (1/4)

The ratio of the surface areas of the balloons = 1: 4

**Video Solution:**

## The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

### Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.4 Question 4:

**Summary:**

It is given that radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. We have found that the ratio of the surface areas of the balloons in the two cases is 1: 4.