Question

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

Answer 1

We have the formula for area of circle,

$Area=\pi r^2$, where $r$ is the radius of the circle

Let, the circle whose area is equal to the sum of the areas of the two circles of radii $24cm$ and $7cm$ be $A_3$ and its radius be $r_3$

Area of circle with radius,$r_1=24cm$ be $A_1$

Area of circle with radius,$r_2=7cm$ be $A_2$

Given,

$A_3=A_1+A_2$

$\pi (r_3{)}^2=\pi (r_1{)}^2+\pi (r_2{)}^2$

$\pi (r_3{)}^2=\pi [(r_1{)}^2+(r_2{)}^2]$

$(r_3{)}^2=(r_1{)}^2+(r_2{)}^2$

$(r_3{)}^2=(24{)}^2+(7{)}^2=625={25}^2$

$r_3=25$

$Diameter=2\times radius=2\times 25=50cm$