Question

The radii of two circles are 15 cm and 8 cm respectively. Find the radius of the circle having area equal
to the sum of the area of the two circles.​

Answer 1

Step-by-step explanation:

Given:-

The radii of two circles are 15 cm and 8 cm respectively.

To find:-

Find the radius of the circle having area equal to the sum of the area of the two circles.

Solution:-

Given that

The two radii of two circles are 15 cm and 8 cm

Let the radius of the first circle be 15 cm

Let the radius of the second circle be 8 cm

r1 = 15 cm

r2 = 8 cm

We know that

Area of a circle whose radius is r units is

πr^2 sq.units

Area of the first circle = πr1^2 sq.cm

=>Area of the first circle = π(15)^2 sq.cm

Area of the first circle = 225π sq.cm--------(1)

Area of the second circle = πr2^2 sq.cm

=>Area of the second circle = π(8)^2 sq.cm

Area of the second circle = 64π sq.cm ------(2)

Sum of the two areas of the two circles

=>(225π+64π) sq.cm

=>289π sq.cm------(3)

Let the radius of the required circle be R cm

Area of the given circle = πR^2 sq.cm

According to the given problem

Area of the required circle = Sum of the areas of the two circles

=>πR^2 = 289π

On cancelling π both sides then

=>R^2 = 289

=>R^2 = 17^2

=>R=17 cm

Radius = 17 cm

Answer :-

Radius of the required circle is 17 cm

Used formula:-

• Area of a circle whose radius is r units is

πr^2 sq.units