Question

The radii of two circles are 9 cm and 12 cm. The circumference of a circle whose area is equal to sum of the areas of the two circles is:

• A. $15cm$
• B. $15\pi cm$
• C. $30\pi cm$
• D. $225cm$

Answer 1

The correct option is C

$30\pi cm$

Step 1: Given data

As per data given in the question,

Radius of two circles are $9cm$ and $12cm$

So, area of first circle $=\pi r^2=\pi \times 9^2=81\pi$

Area of second circle $=\pi r^2=\pi \times {12}^2=144\pi$

As we have to determine the circumference of circle whose area is equal to sum of first two circle.

So, Area of third circle $=225\pi$

Step 2: Applying the formula of circumference and area of circle

Let radius of third circle$=R$

So,

$$\begin{gathered} \pi R^2=225\pi \\ \Rightarrow R^2=225 \\ \Rightarrow R=15cm \end{gathered}$$

Hence. Circumference of the circle will be $=2\times \pi \times 15=30\mathrm{\pi }cm$

Hence, option (c) is correct choice.