Question

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

• A. $1/4^{th}$
• B. $1/3^{rd}$
• C. $1/6^{th}$
• D. $1/9^{th}$

Answer 1

The correct option is A $1/4^{th}$

Let radius of sphere be ${}^{\prime }{r}^{\prime }$ then

$SA=4\pi r^2$

If radius is halved, then

$SA=4\pi {\left(\frac{r}{2}\right)}^2=\frac{1}{4}\times 4\pi r^2$

$=\frac{1}{4}\times$ old surface area

$\therefore \frac{1}{4}th$ change is surface area.