Question

Q. The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. ​

Answer 1

Answer:

10cm

Step-by-step explanation:

Given that

Radius of 1st circle r1=8 cm

Radius of 2nd circle r2=6 cm

We know that the area of the circle of radius r cm

is given by πr2 cm2

So, the area of 1st circle =πr12 cm2=π(8)2 cm2=64π cm2

And the area of 2nd circle =πr22 cm2=π(6)2 cm2=36π cm2

Let r  be the radius of required circle

Area of the required circle i.e., πr2 cm2

= Area of the 1st circle + Area of the 2nd circle

So, we have

πr2 cm2=64π cm2+36π cm2πr2 cm2=(64+36)π cm2r2=100∴r=10 cm

Thus, the radius of the required circle is 10 cm.