The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20 cm is
a. 56 cm
b. 42 cm
c. 28 cm
d. 16 cm

Solution:

Given, the diameter of two circles are 36 cm and 20 cm.

We have to find the radius of a circle whose circumference is equal to the sum of the circumference of given circles.

Circumference of circle = 2πr

Circumference of circle with diameter 36 cm = 2π(36/2)

= 36π

Circumference of circle with diameter 20 cm = 2π(20/2)

= 20π

Sum of circumference of circles = 36π + 20π

= 56π

Let the required radius be R

Circumference = 2πR

Given, 2πR = 56π

2R = 56

R = 28 cm

Therefore, the radius of the circle is 28 cm.

✦ Try This: The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 22cm and 12 cm is

Given, the diameter of two circles are 22 cm and 12 cm.

We have to find the radius of a circle whose circumference is equal to the sum of the circumference of given circles.

Circumference of circle = 2πr

Circumference of circle with diameter 22 cm = 2π(22/2)

= 22π

Circumference of circle with diameter 12 cm = 2π(12/2)

= 12π

Sum of circumference of circles = 22π + 12π

= 34π

Let the required radius be R

Circumference = 2πR

Given, 2πR = 34π

2R = 34

R = 17 cm

Therefore, the radius of the circle is 17 cm.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12

---

NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 9

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20 cm is a. 56 cm, b. 42 cm, c. 28 cm, d. 16 cm

Summary:

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36cm and 20 cm is 28 cm

---

☛ Related Questions:

• The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 . . . .
• Area of a segment of a circle = area of the corresponding sector - area of the corresponding triangl . . . .
• In Fig. 11.2, a circle is inscribed in a square of side 5 cm and another circle is circumscribing th . . . .