Question

Radii of two circles are 3 m and 4 m respectively. Find the radius of a circle having area equal to the sum of the areas of these two circles.

Answer 1

Area of the circle with radius (r) 3 m = $\pi$r²
= 3.14× (3 m)²
= 28.26 m²
Area of the circle with radius (r₁ ) 4 m =$\pi$r₁²
= 3.14× (4 m)²
= 50.24 m²
Now, area of the circle with radius r₂ = area of the circle with radius 3 m + area of the circle with radius 4 m
i.e., $\pi$r₂² = (28.26 + 50.24) m²
$\Rightarrow$ 3.14 ×r₂²= 78.5
$\Rightarrow$ r₂²= $\frac{78.5}{3.14}$
$\Rightarrow$ r₂² = 25
$\Rightarrow$ r₂= 5 m
∴ The radius of the required circle is 5 m.