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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