Question

the radius of a spherical balloon increase from 7cm to 14cm as air is being pumped into it find the ratio of surface area of the balloon in the two cases

Answer 1

FIRST CASE
Radius = 7 cm.
Surface Area = 4πr²
= 4× π × 7 ×7 sq.cm.
SECOND CASE
Radius = 14cm.
Surface Area = 4×π×14×14sq.cm.
Ratio = 4×π×7×7 : 4×π×14×14
= 7×7:14×14
=1:4

Answer 2

Sol. In first of the balloon = 7cm

Radius of balloon =

$= 4\pi {r}^{2}$

$= 4\pi. {1}^{2} sq.cm$

In second condition :

Radius of balloon R2 = 14 cm

Then, surface area C2 =

$c2 = 4\pi {r}^{2}$

$= 4\pi.(14 {)}^{2} sq.cm$

Then,

$\frac{c1}{c2} = \frac{4\pi. {7}^{2} }{4\pi.(14 {)}^{2} }$

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

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

$= \frac{1}{4}$

Hence, C1 : C2 = 1:4