Question

If the radius of a sphere is halved ,what will be the change in its surface area ?

Answer 1

We know SA of a sphere is S1 =4πR2 .
When the radius is halved ,the new SA is S2=4π(R/2)2 = 4πR2 /4 =S1 /4
The new SA S2 is 1/4th of the original SA S1

Answer 2

Given :

the radius of a sphere is halved

To Find :

what will be the change in its surface area ?

Solution:

Let the radius of sphere be r

Surface area of sphere = $4 \pi r^2 = 4 \times \pi \times r^2$

Radius of sphere is halved

So, New radius = $\frac{r}{2}$

Surface area of new sphere =$4 \times \pi \times (\frac{r}{2})^2 = 4 \times \pi \times \frac{r^2}{4}$

So, Surface area of new sphere =$\frac{1}{4}( 4 \times \pi \times r^2)$

So, Surface area of new sphere is one fourth of surface area of original sphere