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

Answer:

Radius of the larger circle is approximately 4.52 m.

Step-by-step 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;

$\frac{5\pi r^2}{5\pi}=\frac{80}{5\pi}\\\\r^2 = 5.09$

Taking square root on both side we get;

$\sqrt{r^2} =\sqrt{5.09}\\ \\r = \sqrt{5.09}\\\\r =2.26 \ m$

Now radius of larger circle = $2x =2\times 2.26 = 4.52\ m$

Hence Radius of the larger circle is approximately 4.52 m.