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

Options

• 34
  
  

• 26

•  17

• 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 

\[\Rightarrow \pi \left( \frac{d}{2} \right)^2 = \pi \left( \frac{10}{2} \right)^2 + \pi \left( \frac{24}{2} \right)^2 \]
\[ \Rightarrow \left( \frac{d}{2} \right)^2 = \left( 5 \right)^2 + \left( 12 \right)^2\]

\[\Rightarrow \left( \frac{d}{2} \right)^2 = 25 + 144\]
\[ \Rightarrow \left( \frac{d}{2} \right)^2 = {13}^2 \]
\[ \Rightarrow \frac{d}{2} = 13\]
\[ \Rightarrow d = 26 cm\]