Question

If the area of a circle is equal to sum of the areas of two circles of diameters $10$ cm and $24$ cm, then the diameter of the larger circle (in cm)is:

• A. $34$
• B. $26$
• C. $17$
• D. $14$

Answer 1

Answer: (B)

$26$

Radius of the first circle $r_1=\frac{10}{2}=5$ cm.

Radius of the second circle $r_2=\frac{24}{2}=12$ cm.

$\therefore$ Sum of their area = $\pi {r_1}^2+\pi {r_2}^2$

$=\pi 5^2+\pi {12}^2$

$=25\pi +144\pi =169\pi$.

Let the radius of the larger circle be $r$.

$\therefore Area=\pi r^2$.

According to the question:

$\Rightarrow \pi r^2=169\pi$

$\Rightarrow r^2=169$

$\Rightarrow r=\sqrt{169}=13$ cm

$\therefore$Radius of the large circle$=13$ cm.

Then, diameter of the larger circle$=13\times 2=26$ cm.

Therefore, option $B$ is correct.