The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 𝑐𝑚 and 7 𝑐𝑚 is

We are given the radii of two circles, Radius of first circle, 𝑟1 = 24 𝑐𝑚

And radius of second circle, 𝑟2 = 7 𝑐𝑚

We have to find the diameter of a third circle, whose area is equal to the sum of the areas of the above two circles.

Now, the area of the first circle A_{1 =} ${{\mathrm{\pi r}}^2}_1$

𝐴₁  = π × 24 × 24 = 576π 𝑐𝑚²

Area of the second circle A_{2 =}  π × 7 × 7 = 49π 𝑐𝑚²

Now, the area of the third circle = sum of the area of two circles

 𝐴 = 576π + 49π

⇒ 𝐴 = 625π 𝑐𝑚²

Let the radius of the circle be 𝑟. So, π𝑟² = 625π

Neglecting π from both sides, we get

𝑟²   = 625

⇒ 𝑟 = $\sqrt{625}$

⇒ 𝑟 = 25 𝑐𝑚

Now, the diameter of the circle, 𝑑 = 2 × 𝑟

⇒ 𝑑 = 2 × 25

⇒ 𝑑 = 50 𝑐𝑚

So, the diameter of the required circle is 50 𝑐𝑚