Question

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

(a) 34

(b) 26

(c) 17

(d) 14

Answer 1

Let the diameter of the larger circle be d
Now, Area of larger circle = Area of circle having diameter 10 cm + Area of circle having diameter 24 cm
$$\begin{gathered} \Rightarrow \mathrm{\pi }{\left(\frac{d}{2}\right)}^2=\mathrm{\pi }{\left(\frac{10}{2}\right)}^2+\mathrm{\pi }{\left(\frac{24}{2}\right)}^2 \\ \Rightarrow {\left(\frac{d}{2}\right)}^2={\left(5\right)}^2+{\left(12\right)}^2 \end{gathered}$$

$$\begin{gathered} \Rightarrow {\left(\frac{d}{2}\right)}^2=25+144 \\ \Rightarrow {\left(\frac{d}{2}\right)}^2={13}^2 \\ \Rightarrow \frac{d}{2}=13 \\ \Rightarrow d=26\mathrm{cm} \end{gathered}$$
Hence, the correct answer is option (b).