Question

Find the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm. [CBSE 2011]

Answer 1

Let the diameter of the required circle be d.
Now, Area of the required circle = Area of circle having radius 4 cm + Area of circle having radius 3 cm

$$\begin{gathered} \Rightarrow \mathrm{\pi }{\left(\frac{d}{2}\right)}^2=\mathrm{\pi }{\left(4\right)}^2+\mathrm{\pi }{\left(3\right)}^2 \\ \Rightarrow {\left(\frac{d}{2}\right)}^2=16+9 \\ \Rightarrow {\left(\frac{d}{2}\right)}^2=25={\left(5\right)}^2 \\ \Rightarrow \frac{d}{2}=5 \\ \Rightarrow d=10\mathrm{cm} \end{gathered}$$

Hence, the diameter of the circle is 10 cm.