Question

If the diameter of the sphere is doubled, the surface area of the resultant sphere becomes $x$ times that of the original one. Then, $x$ would be:

• A. $3$
• B. $2$
• C. $4$
• D. $8$

Answer 1

Answer: (C)

Let $S_1$ be the original surface area of the sphere and $S_2$ be the surface area with double the diameter.

Doubling the diameter means doubling the radius.

Let $r_1$ and $r_2$ corresponding radii.

We know that $S=4\pi r^2$ and $r_2=2r_1$ ....(Given)

Hence, $\frac{S_1}{S_2}=\frac{4\pi r_1^2}{4\pi r_2^2}$

$\Rightarrow \frac{S_1}{S_2}=\frac{r_1^2}{(2r_1{)}^2}$

$\Rightarrow S_2=4S_1$.