Question

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 ______.

Options

• 1 : 4

• 1 : 3

• 2 : 3

• 2 : 1

Answer 1

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.

Explanation:

Given that radius of a hemispherical balloon (r₁) = 6 cm

Since, air is pumped into balloon.

Then, radius of hemispherical balloon (r₂) = 12 cm

∴ Ratio of the surface areas of the balloon in both cases = `(3pir_1^2)/(3pir_2^2)`

 `\implies r_1^2/r_2^2 = (6)^2/(12)^2`

= `36/144`

= `1/4`

= 1 : 4

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