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Solution:
Using the formula of the circumference of circle C = 2πr, we find the radius of the circle.
Radius (r₁) of the 1st circle = 19 cm
Radius (r₂) of the 2nd circle = 9 cm
Let the radius of the 3rd circle be r.
Circumference of the 1st circle = 2πr₁ = 2π (19) = 38π
Circumference of the 2nd circle = 2πr₂ = 2π (9) = 18π
Circumference of the 3rd circle = 2πr
Given that,
Circumference of the 3rd circle = Circumference of the 1st circle + Circumference of the 2nd circle
2πr = 38π + 18π
2πr = 56π
r = 56π/2π
r = 28
Therefore, the radius of the circle that has a circumference equal to the sum of the circumference of the two given circles is 28 cm.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 12
Video Solution:
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
NCERT Solutions Class 10 Maths Chapter 12 Exercise 12.1 Question 1
Summary:
If the radius of two circles are 19 cm and 9 cm respectively, the radius of the circle which has a circumference equal to the sum of the circumferences of the two circles is 28 cm.
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