Question

The radius of a hemispherical balloon increases from $6cm$ to $12cm$ 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) $1:2$

Answer 1

In First case, the radius of the balloon $=6cm$
In Second case, the radius of the balloon $=12cm$.
Now, Surface Area of a hemisphere $=3\pi$(radius)${}^2$
So, the ratio of the surface area's will be $=3\pi (6{)}^2:3\pi (12{)}^2$
$=6^2:{12}^2$
$=36:144$
$=1:4$
Hence, the correct option is (a)