Question

The radius of a spherical balloon increases from $7cm$ to $14cm$ as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases.

• A. $1:8$
• B. $1:9$
• C. $5:8$
• D. None of these

Answer 1

The correct option is A $1:8$

We have,

$r=$ radius of balloon $=7cm$

$R=$ radius of pumped balloon $=14cm$

So, the ratio of the volume of sphere before inflated $/$ volume of spherical balloon after inflated

$=\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}$

$=\frac{7^3}{(14{)}^3}$

$=\frac{7\times 7\times 7}{14\times 14\times 14}$

$=\frac{1\times 1\times 1}{2\times 2\times 2}$

$=\frac{1}{8}$

Hence, this is the answer.