The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it.

Question:

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

Solution:

(a)  1 : 4

Ratio of the surface areas of balloon $=\frac{2 \pi \times 6^{2}}{2 \pi \times 12^{2}}=\frac{36}{144}=\frac{1}{4}$

 

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