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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)50 cm
- b)31 cm
- c)62 cm
- d)25 cm
Correct answer is option 'A'. Can you explain this answer?
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The diameter of a circle whose area is equal to the sum of the areas o...
Given:
Radius of first circle = 24 cm
Radius of second circle = 7 cm
We need to find the diameter of a circle whose area is equal to the sum of the areas of the two circles.
Formula for the area of a circle:
Area = πr^2
Let's calculate the areas of the two circles first.
Area of the first circle = π(24)^2
= 576π cm^2
Area of the second circle = π(7)^2
= 49π cm^2
Now, we need to find the diameter of a circle whose area is equal to the sum of the areas of the two circles.
Sum of the areas of the two circles = 576π + 49π
= 625π cm^2
To find the diameter, we can use the formula for the area of a circle:
Area = πr^2
Let's substitute the given area into the formula:
625π = πr^2
Dividing both sides by π:
625 = r^2
Taking the square root of both sides:
r = √625
r = 25 cm
Since the radius is 25 cm, the diameter will be twice the radius:
Diameter = 2r
= 2(25)
= 50 cm
Therefore, the diameter of the circle whose area is equal to the sum of the areas of the two circles is 50 cm, which corresponds to option A.
Radius of first circle = 24 cm
Radius of second circle = 7 cm
We need to find the diameter of a circle whose area is equal to the sum of the areas of the two circles.
Formula for the area of a circle:
Area = πr^2
Let's calculate the areas of the two circles first.
Area of the first circle = π(24)^2
= 576π cm^2
Area of the second circle = π(7)^2
= 49π cm^2
Now, we need to find the diameter of a circle whose area is equal to the sum of the areas of the two circles.
Sum of the areas of the two circles = 576π + 49π
= 625π cm^2
To find the diameter, we can use the formula for the area of a circle:
Area = πr^2
Let's substitute the given area into the formula:
625π = πr^2
Dividing both sides by π:
625 = r^2
Taking the square root of both sides:
r = √625
r = 25 cm
Since the radius is 25 cm, the diameter will be twice the radius:
Diameter = 2r
= 2(25)
= 50 cm
Therefore, the diameter of the circle whose area is equal to the sum of the areas of the two circles is 50 cm, which corresponds to option A.
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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 isa)50 cmb)31 cmc)62 cmd)25 cmCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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 isa)50 cmb)31 cmc)62 cmd)25 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 isa)50 cmb)31 cmc)62 cmd)25 cmCorrect answer is option 'A'. Can you explain this answer?.
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 isa)50 cmb)31 cmc)62 cmd)25 cmCorrect answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about 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 isa)50 cmb)31 cmc)62 cmd)25 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 isa)50 cmb)31 cmc)62 cmd)25 cmCorrect answer is option 'A'. Can you explain this answer?.
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