# Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm

**Solution:**

Given, two __circles__ of diameters 20 cm and 48 cm.

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

__Area of circle__ = πr²

Diameter of circle = 20 cm

Radius = 20/2 = 10 cm

Area of circle with radius 10 cm = π(10)²

= 100π

Diameter of circle = 48 cm

Radius = 48/2 = 24 cm

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

= 576π

Sum of the areas = 100π + 576π

= π(676)

Let the required radius be R.

Area of circle with radius R = πR²

Given, πR² = π(676)

R² = 676

Taking square root,

R = 26 cm

Diameter = 2R

= 2(26)

= 52 cm

Therefore, the required diameter is 52 cm.

**✦ Try This: **Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 10 cm and 24 cm.

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

**NCERT Exemplar Class 10 Maths Exercise 11.3 Sample Problem 1**

## Find the diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm

**Summary:**

The diameter of the circle whose area is equal to the sum of the areas of the two circles of diameters 20 cm and 48 cm is 52 cm

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