Question

The sum of the areas of two circle $A$ and $B$ is equal to the area of a third circle $C$, whose diameter is $30$ cm. If the diameter of circle $A$ is $18$ cm, then the radius of circle $B$ is:

• A. $18$ cm
• B. $15$ cm
• C. $12$ cm
• D. $10$ cm

Answer 1

The correct option is C $12$ cm

We know that diameter is twice the radius.

So the Radius of $A$ and $C$ are $9cm$ and $15cm$, respectively

Let the radius of the circle $B=r$.

We know, area of a circle equals $\pi r^2$.

$\therefore$ According to the given condition

$\pi (9{)}^2+\pi r^2=\pi {15}^2$

$⟹$ $(9{)}^2+r^2={15}^2$.

On Solving we get,

$⟹$$r^2={15}^2-9^2=225-81=144c{m}^2$.

$⟹$$r=12cm$.

Therefore, option $C$ is correct.