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The ratio of area of two circles whose ratio of circumference is 3:1 will be
- a)3 : 1
- b)1 : 3
- c)1 : 9
- d)9 : 1
Correct answer is option 'D'. Can you explain this answer?
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The ratio of area of two circles whose ratio of circumference is 3:1 w...
Ratio of Circumference of two circles:
The ratio of the circumference of two circles can be given as follows:
C1 : C2 = 3 : 1
Relation between circumference and diameter:
The circumference of a circle can be calculated using the formula:
C = πd
where C is the circumference and d is the diameter.
Relation between circumference and radius:
The circumference of a circle can also be calculated using the formula:
C = 2πr
where C is the circumference and r is the radius.
Deriving the relation between radius and diameter:
We know that the diameter of a circle is twice the radius. Therefore, we can write:
d = 2r
Calculating the ratio of the radii:
Let the radii of the two circles be r1 and r2 respectively.
We can express the radii in terms of the diameters as follows:
r1 = d1/2 and r2 = d2/2
Substituting the values of r1 and r2 in the given ratio of circumferences:
2πr1 : 2πr2 = 3 : 1
πd1/2 : πd2/2 = 3 : 1
d1/2 : d2/2 = 3 : 1
d1 : d2 = 3 : 1
Calculating the ratio of the areas:
The area of a circle can be calculated using the formula:
A = πr^2
Let the areas of the two circles be A1 and A2 respectively.
We can express the areas in terms of the radii as follows:
A1 = πr1^2 and A2 = πr2^2
Substituting the values of r1 and r2 in the above expressions:
A1 = π(d1/2)^2 and A2 = π(d2/2)^2
A1 = πd1^2/4 and A2 = πd2^2/4
Taking the ratio of the areas:
A1 : A2 = (πd1^2/4) : (πd2^2/4)
A1 : A2 = d1^2 : d2^2
A1 : A2 = (d1 : d2)^2
A1 : A2 = (3 : 1)^2
A1 : A2 = 9 : 1
Therefore, the ratio of the areas of the two circles is 9 : 1. Hence, option D is correct.
The ratio of the circumference of two circles can be given as follows:
C1 : C2 = 3 : 1
Relation between circumference and diameter:
The circumference of a circle can be calculated using the formula:
C = πd
where C is the circumference and d is the diameter.
Relation between circumference and radius:
The circumference of a circle can also be calculated using the formula:
C = 2πr
where C is the circumference and r is the radius.
Deriving the relation between radius and diameter:
We know that the diameter of a circle is twice the radius. Therefore, we can write:
d = 2r
Calculating the ratio of the radii:
Let the radii of the two circles be r1 and r2 respectively.
We can express the radii in terms of the diameters as follows:
r1 = d1/2 and r2 = d2/2
Substituting the values of r1 and r2 in the given ratio of circumferences:
2πr1 : 2πr2 = 3 : 1
πd1/2 : πd2/2 = 3 : 1
d1/2 : d2/2 = 3 : 1
d1 : d2 = 3 : 1
Calculating the ratio of the areas:
The area of a circle can be calculated using the formula:
A = πr^2
Let the areas of the two circles be A1 and A2 respectively.
We can express the areas in terms of the radii as follows:
A1 = πr1^2 and A2 = πr2^2
Substituting the values of r1 and r2 in the above expressions:
A1 = π(d1/2)^2 and A2 = π(d2/2)^2
A1 = πd1^2/4 and A2 = πd2^2/4
Taking the ratio of the areas:
A1 : A2 = (πd1^2/4) : (πd2^2/4)
A1 : A2 = d1^2 : d2^2
A1 : A2 = (d1 : d2)^2
A1 : A2 = (3 : 1)^2
A1 : A2 = 9 : 1
Therefore, the ratio of the areas of the two circles is 9 : 1. Hence, option D is correct.
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The ratio of area of two circles whose ratio of circumference is 3:1 will bea)3 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'D'. 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 ratio of area of two circles whose ratio of circumference is 3:1 will bea)3 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'D'. 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 ratio of area of two circles whose ratio of circumference is 3:1 will bea)3 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'D'. Can you explain this answer?.
The ratio of area of two circles whose ratio of circumference is 3:1 will bea)3 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'D'. 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 ratio of area of two circles whose ratio of circumference is 3:1 will bea)3 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'D'. 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 ratio of area of two circles whose ratio of circumference is 3:1 will bea)3 : 1b)1 : 3c)1 : 9d)9 : 1Correct answer is option 'D'. Can you explain this answer?.
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