The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is
a. 1 : 4
b. 1 : 3
c. 2 : 3
d. 2 : 1

Solution:

Given, the radius of a hemispherical balloon increase from 6 cm to 12 cm

We have to find the ratio of the surface areas of the balloon in the two cases.

Surface area of hemisphere = 3πr²

When r = 6 cm

Surface area = 3π(6)²

= 3π(36)

= 108π cm²

When r = 12 cm

Surface area = 3π(12)²

= 3π(144)

= 432π cm²

Ratio of surface area = 108π / 432π

= 108 / 432

= 1/4

Therefore, the required ratio is 1 : 4

✦ Try This: The radius of a hemispherical balloon increases from 8 cm to 14 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 13

NCERT Exemplar Class 9 Maths Exercise 13.1 Problem 10

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is a. 1 : 4, b. 1 : 3, c. 2 : 3, d. 2 : 1

Summary:

The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is 1 : 4

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