Question

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.

Answer 1

R = radius of ballon = 7cm
r = radius of pumped ballon = 14cm

surface area of sphere before inflated / urface area of spherical ballon after inflated

=4×(22/7)×R×R / 4 × (22/7) × r×r
= R×R/r×r
=7×7/14×14
= 49 / 196
= 1:4

Answer 2

The ratio of surface areas of the balloon in the two cases is 1:4.

GIVEN:- Radius of a spherical balloon increases from 7 cm to 14 cm

TO FIND:- The ratio of surface areas of the balloon in the two cases.

SOLUTION:-

As we know, the Surface area of the sphere = 4πr², where r is the radius of the sphere.

The surface area of the spherical balloon, when the radius is 7 cm.

The surface area of the sphere = 4πr²

$= 4 \times \frac{22}{7} \times {7}^{2} \\ = 4 \times 22 \times 7 \\ = 616 \: {cm}^{2}$

The surface area of the spherical balloon, when the radius is 14 cm.

$= 4 \times \frac{22}{7} \times {14}^{2} \\ = 2464 {cm}^{2}$

The ratio of the surface area of the balloon in both cases = Surface area of the balloon in the first case ÷ Surface area of the balloon in the second case

$= \frac{616}{2464} \\ = \frac{1}{4}$

Which is equal to 1:4

Hence, the ratio of surface areas of the balloon in the two cases is 1:4.

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