Question

The diameter of a spherical balloon increases from 14 cm. to 28 cm. as air is being pumped into it. Find the ratio of surface areas of the balloons in the two cases.

Answer 1

The diameter of the balloon, d = 14 cm

Thus, its radius, r = d/2 = 14/2 = 7 cm

∴ Surface area = 4πr² = 4 × 22/7 x 7 x 7

= 88 × 7 = 616cm²

When air is pumped, the diameter = 28 cm 

thus its radius = d/2 = 28/2 = 14 cm

Its surface area = 4πr²

= 4 × 22/7 × 14 × 14

= 88 × 28 = 2464 cm² 

Ratio of areas = 616 : 2464 

= 1 : 4

(OR)

Original radius = 14/2 = 7cm

Increased radius = 28/2 = 14 cm

Ratio of areas = r₁² : r₂² 

= 7² : 14² 

= 7 × 7 : 14 × 14 

= 1:4