# The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is

a. 31 cm

b. 25 cm

c. 62 cm

d. 50 cm

**Solution:**

Given, the radii of two circles are 24 cm and 7 cm.

We have to find the __diameter of a circle__ whose area is equal to the sum of the areas of two circles.

__Area of circle__ = πr²

Area of circle with radius 24 cm = π(24)²

= 576π

Area of circle with radius 7 cm = π(7)²

= 49π

Sum of the area of two circles = 576π + 49π

= 625π

Let the required diameter be D

Radius = D/2

Area of circle with radius D/2 = π(D/2)²

= πD²/4

Given, πD²/4 = 625π

D²/4 = 625

D² = 625(4)

Taking __square root__,

D = 25(2)

D = 50 cm

Therefore, the diameter of circle is 50 cm

**✦ Try This:** If the area of circle is 176 cm², find the circumference of the circle.

Given, area of circle = 176 cm²

We have to find the circumference of the circle.

Area of circle = πr²

176 = (22/7)r²

r² = 176(7)/22

= 8(7)

r² = 56

Taking square root,

r = √56

r = 7.5 cm

__Circumference of circle__ = 2πr

= 2(22/7)(7.5)

= 15(22/7)

= 47.14 cm

Therefore, the circumference of the circle is 47.14 cm

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

**NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 10**

## The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is a. 31 cm, b. 25 cm, c. 62 cm, d. 50 cm

**Summary:**

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is 50 cm

**☛ Related Questions:**

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- Is the area of the circle inscribed in a square of side a cm, πa² cm²? Give reasons for your answer

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