Question

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm? [CBSE 2012]

Answer 1

Let the diameter of the required circle be d.
Now, Area of required circle = Area of circle having diameter 10 cm + Area of circle having diameter 24 cm

$$\begin{gathered} \Rightarrow \mathrm{\pi }{\left(\frac{d}{2}\right)}^2=\mathrm{\pi }{\left(\frac{10}{2}\right)}^2+\mathrm{\pi }{\left(\frac{24}{2}\right)}^2 \\ \Rightarrow {\left(\frac{d}{2}\right)}^2=25+144 \\ \Rightarrow {\left(\frac{d}{2}\right)}^2={13}^2 \\ \Rightarrow \frac{d}{2}=13 \\ \Rightarrow d=26\mathrm{cm} \end{gathered}$$
Hence, the diameter of the of the circle is 26 cm.