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 = 4πr2
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
☛ Check: NCERT Solutions for Class 9 Maths Chapter 13
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.
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