Question

The diameter of a circle whose area is equal to the sum of the area of two circles of diameter $16cm$ and $12cm$ is:

• A. $56cm$
• B. $42cm$
• C. $28cm$
• D. $20cm$

Answer 1

Answer: (D)

$20cm$

Let radius of new circle be $R$

Radius of first circle $=\frac{16}{2}=8$ cm

Area of first circle $=\pi \times r^2=64\pi {cm}^2$

Radius of second circle $=\frac{12}{2}=6$ cm

Area of second circle $=\pi \times r^2=36\pi {cm}^2$

Area of new circle $=64\pi +36\pi$

$\pi R^2=100\pi R^2=100R=\sqrt{100}=10cm$