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

Solution:

Using the formula of area of circle A = πr², we can find the radius of the circle.

The radius of the 1^st circle = 8 cm

The radius of the  2^nd circle = 6 cm

Let the radius of the 3 ^rd circle be equal to r.

Area of the 1^st circle = πr₁²= π(8)² = 64π sq.cm ------------ (1)

Area of the 2^nd circle = πr₂² = π(6)² = 36π sq.cm ----------- (2)

Given that, Area of the 3^rd circle = Area of the 1^st circle + Area of the 2^nd circle

πr² = πr₁² + πr₂²

πr² = 64π + 36π [From equation (1) and (2)]

πr² = 100π

r² = 100

r = ± 10

However, the radius cannot be negative. Thus, r = 10

Therefore, the radius of the circle having an area equal to the sum of the areas of the two circles is 10 cm.

☛ Check: NCERT Solutions Class 10 Maths Chapter 12

Video Solution:

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.

NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 2

Summary:

The radius of the circle having an area equal to the sum of the areas of the two circles of radii 8 cm and 6 cm respectively is 10 cm.

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