Question

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

Answer 1

Let the radius of the first circle be r1
and second circle be r2.
third circle be R.
Given,
r1=8cm.r2=6cm.
A/q.
phi R^2=phi r1^2+phi r2^2.
phi R^2=phi(8^2+6^2).
R^2=64+36
R^2=100
R=10.
therefore the radius of the third circle of 10.CM.

HOPE IT HELPS YOU

Answer 2

Answer:

The radius of the circle is 10cm

Step-by-step explanation:

We have 2 circles, whose radii are 8cm and 6cm respectively.

We then have a bigger circle whose area is the sum of the areas of these smaller circles. So we have to find the areas of these circles and then add them.

The area of a circle = π ×r×r

So the area of the first circle is

π × 8cm × 8cm = 201.088 squared cm

The area of the second circle is

π × 6cm × 6cm = 113.112 squared cm

When we add the areas of these two circles;

208.088 + 113.112 = 314.2 squared cm

314.2 squared cm is the area of the big circle, yet we need its radius.

314.2 = π × r × r

π = 3.142

So we evaluate

314.2 = 3.142 × squared r

Dividing both sides by 3.142, we get

100 = squared r

We then get the square roots of both sides

√100 = √ squared r

The square root of 100 is 10cm.

Hence r = 10cm.