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If the ratio of circumferences of two circles is 4:9, what is the ratio of their areas?
- a)9:4
- b)16:81
- c)4:9
- d)2:3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If the ratio of circumferences of two circles is4:9,what is the ratio ...
2πr1/2πr2 = 4/9
r1/r2 = 4/9
πr12/πr22 = r12/r22 = 16/81
r1/r2 = 4/9
πr12/πr22 = r12/r22 = 16/81
Most Upvoted Answer
If the ratio of circumferences of two circles is4:9,what is the ratio ...
According to question the circles circumstances are
one is 4 and other is 9
then circumstance = 2πr
2πr=4. 2πr=9. ('r' is the radius of the circle)
2×22/7r=4. 2×22/7r=9
r=4×7/44. r=9×7/44
r=28/44. r=63/44
So area of the circle = π×r×r
area=22/7×(28/44)² 22/7×(63/44)²
similarly the ratio of the circles is
22/7×(28/44)² /22/7×(63/44)² [22/7/22/7=1]
So 28²×44²/63²×44². { 44²/44²=1}
so 28²/63²=(2²×2²×7²)/(3²×3²×7²). [7²/7²=1]
Then 2²×2²/3²×3².
so. 4²/9². = 16/81 =16:81
So the answer is 16:81
I hope it is helpful for understanding this question's answer.
one is 4 and other is 9
then circumstance = 2πr
2πr=4. 2πr=9. ('r' is the radius of the circle)
2×22/7r=4. 2×22/7r=9
r=4×7/44. r=9×7/44
r=28/44. r=63/44
So area of the circle = π×r×r
area=22/7×(28/44)² 22/7×(63/44)²
similarly the ratio of the circles is
22/7×(28/44)² /22/7×(63/44)² [22/7/22/7=1]
So 28²×44²/63²×44². { 44²/44²=1}
so 28²/63²=(2²×2²×7²)/(3²×3²×7²). [7²/7²=1]
Then 2²×2²/3²×3².
so. 4²/9². = 16/81 =16:81
So the answer is 16:81
I hope it is helpful for understanding this question's answer.
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Community Answer
If the ratio of circumferences of two circles is4:9,what is the ratio ...
Understanding the problem
To solve this problem, we need to understand the relationship between the circumference and area of a circle. The circumference of a circle is the distance around its boundary, while the area of a circle is the measure of the space enclosed by its boundary.
Given information
We are given that the ratio of the circumferences of two circles is 4:9. Let's assume the circumferences of the two circles are 4x and 9x units.
Calculating the ratio of their areas
The formula for the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius. Since the radius is half the diameter, we can also write this formula as C = πd, where d represents the diameter.
Since the ratio of the circumferences is given as 4:9, we can write the equation as:
4x/9x = πd1/πd2
Simplifying this equation, we get:
4/9 = d1/d2
Now, let's consider the formula for the area of a circle, which is A = πr^2. Since the radius is half the diameter, we can also write this formula as A = π(d/2)^2, which simplifies to A = πd^2/4.
Substituting the values of the diameters from the previous equation, we get:
A1/A2 = (πd1^2/4)/(πd2^2/4)
A1/A2 = d1^2/d2^2
Using the equation we obtained earlier, d1/d2 = 4/9, we can substitute this into the area ratio equation:
A1/A2 = (4/9)^2
A1/A2 = 16/81
Answer
Therefore, the ratio of the areas of the two circles is 16:81, which corresponds to option B.
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If the ratio of circumferences of two circles is4:9,what is the ratio of their areas?a)9:4b)16:81c)4:9d)2:3Correct answer is option 'B'. Can you explain this answer?
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If the ratio of circumferences of two circles is4:9,what is the ratio of their areas?a)9:4b)16:81c)4:9d)2:3Correct answer is option 'B'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about If the ratio of circumferences of two circles is4:9,what is the ratio of their areas?a)9:4b)16:81c)4:9d)2:3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the ratio of circumferences of two circles is4:9,what is the ratio of their areas?a)9:4b)16:81c)4:9d)2:3Correct answer is option 'B'. Can you explain this answer?.
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