## 2. 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 area

Question

2. 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.

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3 weeks 2021-10-01T14:05:16+00:00 2 Answers 0 views 0

10

Step-by-step explanation:

area of first circle + area of second circle = final area of circle

8^2 + 6^ 2 = R^ 2

R = 10cm

2. Given:

The radii of two circles are 8 cm and 6 cm.

To be found:

The radius of the circle having an area equal to the sum of the  areas of the two circles.

Here are steps-

• First, we will find the area of the two circles whose radii are given.
• Adding the areas of two circles
• We will get the area of the big circle.
• And with the help of the area formula of the circle.

So,

Area of circle whose radius = 8cm

Area = πr² unit sq. [∵ In which ‘r’ is the ‘radius’ of the circle] Area of circle whose radius = 8cm Now, the sum of the areas of circles will be

= 64π + 36π = 100π units sq.

Therefore,

The area of the big circle = 100π unit sq.

So,

Area of the big circle = 100π unit sq.   ⇒ r = 10 cm

Hence,

The radius of the big circle whose area equal to the sum of the  areas of the two circles = 10 cm.