Question

The sum of the areas of two circles is 80 square meters. Find the length of a radius of each circle if

one of them is twice as long as the other.
What is the radius of the larger circle?

Answer 1

Radius of the larger circle is approximately 4.52 m.

Explanation:

Given:

Sum of area of 2 circle = 80 sq. m

Let the radius of smaller circle be 'r'.

Then Given:

one of them is twice as long as the other.

radius of the Larger circle =
`2r`

we need to find the radius of the larger circle.

Solution:

Now we know that;

Area of the circle is π times square of the radius.

framing in equation form we get;

Area of the smaller circle =
`\pi r^2`

Area of larger circle =
`\pi (2r)^2 =\pi4r^2`

Now given:

Area of the smaller circle + Area of the larger circle = 80

Substituting the values we get;

`\pi r^2+\pi 4r^2=80\\\\5\pi r^2 = 80`

Now Dividing both side by 5π we get;

`(5\pi r^2)/(5\pi)=(80)/(5\pi)\\\\r^2 = 5.09`

Taking square root on both side we get;

`√(r^2) =√(5.09)\\ \\r = √(5.09)\\\\r =2.26 \ m`

Now radius of larger circle =
`2x =2* 2.26 = 4.52\ m`

Hence Radius of the larger circle is approximately 4.52 m.