Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm
Solution:
Given, radii of two circles are 15 cm and 18 cm.
We have to find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles.
Circumference of circle = 2πr
Circumference of circle with radius 15 cm = 2π(15)
= 30π
Circumference of circle with radius 18 cm = 2π(18)
= 36π
Sum of circumference of two circles = 30π + 36π
= 66π
Let the required radius of the circle be R.
Circumference of circle with radius R = 2πR
Given, 2πR = 66π
2R = 66
R = 66/2
R = 33 cm
Therefore, the radius of the new circle is 33 cm.
✦ Try This: Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 8 cm and 10 cm.
Given, radii of two circles are 8 cm and 10 cm.
We have to find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles.
Circumference of circle = 2πr
Circumference of circle with radius 8 cm = 2π(8)
= 16π
Circumference of circle with radius 10 cm = 2π(10)
= 20π
Sum of circumference of two circles = 16π + 20π
= 36π
Let the required radius of the circle be R.
Circumference of circle with radius R = 2πR
Given, 2πR = 36π
2R = 36
R = 36/2
R = 18 cm
Therefore, the radius of the new circle is 18 cm.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.3 Problem 1
Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm
Summary:
The radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii 15 cm and 18 cm is 33 cm
☛ Related Questions:
visual curriculum