Question

If the circumference of a circle increases from $4\pi$ to $8\pi$, then its area is :

• A. Halved
• B. Doubled
• C. Tripled
• D. Quadrupled

Answer 1

Answer: (D)

Quadrupled

Let $C_1$, $r_1$, $A_1$ be the circumference, radius and area of circle with circumference as $4\pi$

Let $C_2$, $r_2$, $A_2$ be the circumference, radius and area of circle with circumference as $8\pi$

Given,

$C_1=4\pi$ and ,$C_2=8\pi$

$\therefore \frac{C_1}{C_2}=\frac{4\pi }{8\pi }$

$\Rightarrow \frac{2\pi r_1}{2\pi r_2}=\frac{4}{8}$

$\Rightarrow \frac{r_1}{r_2}=\frac{1}{2}$

Now,

$\frac{A_1}{A_2}=\frac{\pi {r_1}^2}{\pi {r_2}^2}$

$=>\frac{A_1}{A_2}=(\frac{1}{2}{)}^2$

$\Rightarrow \frac{A_1}{A_2}=\frac{1}{4}$
$\Rightarrow A_2=4A_1$

$\therefore$ Area will be quadrupled.