Question

The radius of a hemispherical balloon changes from $5cm$ to $15cm$. Find the ratio of the surface area of the balloon in the two cases.

Answer 1

Step 1: Find the individual surface area of both the hemisphere.

The surface area of the hemisphere of radius $r$ $=3{\mathrm{\pi r}}^2$

Let $A$ be the surface area of a hemispherical balloon with radius $5cm$ and $B$ be the surface area of a hemispherical balloon with radius $15cm$

Thus, $A=3\mathrm{\pi }{\left(5\right)}^2$

Similarly, $B=3\mathrm{\pi }{\left(15\right)}^2$

Step 2: Find the ratio of both the surface area.

$\frac{A}{B}=\frac{3\mathrm{\pi }{\left(5\right)}^2}{3\mathrm{\pi }{\left(15\right)}^2}$

$\frac{A}{B}=\frac{1}{9}$

Hence, the required ratio is $\frac{1}{9}$.