Question

The radius of a spherical balloon increases from 14 cm to 21 cm as air is pumped into it. Find the ratio of the surface areas of the balloon in the two situations.

Answer 1

Answer:

Ratio of the surface areas of the balloon in the two situations 4:9

Step-by-step explanation:

Surface area of sphere( Balloon)

$= 4\pi {r}^{2} \: {cm}^{2}$

Surface area of sphere when radius is 14 cm

$S_1= 4 \times \frac{22}{7} \times ( {14)}^{2} \\ \\ = 4 \times \frac{22}{7} \times 196 \\ \\ = 88 \times 28 \\ \\ S_1 = 2464 \: {cm}^{2}$

Surface area of sphere when radius increases to 21 cm

$S_2= 4 \times \frac{22}{7} \times ( {21)}^{2} \\ \\ = 4 \times \frac{22}{7} \times 441 \\ \\ = 88 \times 63 \\ \\S_2 = 5544 \: {cm}^{2}$

Ratio of surface area in both the situation

$\frac{S_1}{S_2} = \frac{88 \times 28}{88 \times 63} \\ \\ \frac{S_1}{S_2} = \frac{</strong><strong>4</strong><strong>}{</strong><strong>9</strong><strong>}$

Hope it helps you