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.
Solution:
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
$\Rightarrow \pi\left(\frac{d}{2}\right)^{2}=\pi(4)^{2}+\pi(3)^{2}$
$\Rightarrow\left(\frac{d}{2}\right)^{2}=16+9$
$\Rightarrow\left(\frac{d}{2}\right)^{2}=25=(5)^{2}$
$\Rightarrow \frac{d}{2}=5$
$\Rightarrow d=10 \mathrm{~cm}$
Hence, the diameter of the circle is 10 cm.
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