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The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).
- a)9 : 16
- b)9 : 25
- c)16 : 25
- d)16 : 27
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The area of a circle is proportional to the square of its radius. A sm...
Area of a circle = π(radius)2
A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm.
Area of large circle = π(5)2
= (22/7) × (5)2
= (22 × 5 ×5)/7
= 550/7
Area of small circle = π (3)2
= (22 × 3 × 3)/7
= 198/7
Area of annular zone
= 352/7
The ratio of the area of the annular zone to the area of the larger circle = area of annular zone: area of large circle
= 16: 25
A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm.
Area of large circle = π(5)2
= (22/7) × (5)2
= (22 × 5 ×5)/7
= 550/7
Area of small circle = π (3)2
= (22 × 3 × 3)/7
= 198/7
Area of annular zone
= 352/7
The ratio of the area of the annular zone to the area of the larger circle = area of annular zone: area of large circle
= 16: 25
Most Upvoted Answer
The area of a circle is proportional to the square of its radius. A sm...
To solve this problem, we need to find the areas of both the larger circle and the smaller circle, and then calculate the area of the annular zone by subtracting the smaller circle's area from the larger circle's area. Finally, we can find the ratio of the area of the annular zone to the area of the larger circle.
1. Calculate the area of the larger circle:
The formula to calculate the area of a circle is given by A = πr², where A is the area and r is the radius.
For the larger circle, the radius is given as 5 cm. Therefore, the area of the larger circle is:
A1 = π(5 cm)² = 25π cm²
2. Calculate the area of the smaller circle:
The radius of the smaller circle is given as 3 cm. Therefore, the area of the smaller circle is:
A2 = π(3 cm)² = 9π cm²
3. Calculate the area of the annular zone:
The area of the annular zone is the difference between the area of the larger circle and the area of the smaller circle:
Annular zone area = A1 - A2 = 25π cm² - 9π cm² = 16π cm²
4. Find the ratio of the area of the annular zone to the area of the larger circle:
The ratio is given by the formula:
Ratio = (Area of annular zone) / (Area of larger circle)
Ratio = (16π cm²) / (25π cm²)
Ratio = 16/25
Therefore, the ratio of the area of the annular zone to the area of the larger circle is 16:25, which corresponds to option C.
1. Calculate the area of the larger circle:
The formula to calculate the area of a circle is given by A = πr², where A is the area and r is the radius.
For the larger circle, the radius is given as 5 cm. Therefore, the area of the larger circle is:
A1 = π(5 cm)² = 25π cm²
2. Calculate the area of the smaller circle:
The radius of the smaller circle is given as 3 cm. Therefore, the area of the smaller circle is:
A2 = π(3 cm)² = 9π cm²
3. Calculate the area of the annular zone:
The area of the annular zone is the difference between the area of the larger circle and the area of the smaller circle:
Annular zone area = A1 - A2 = 25π cm² - 9π cm² = 16π cm²
4. Find the ratio of the area of the annular zone to the area of the larger circle:
The ratio is given by the formula:
Ratio = (Area of annular zone) / (Area of larger circle)
Ratio = (16π cm²) / (25π cm²)
Ratio = 16/25
Therefore, the ratio of the area of the annular zone to the area of the larger circle is 16:25, which corresponds to option C.
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The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).a)9 : 16b)9 : 25c)16 : 25d)16 : 27Correct answer is option 'C'. Can you explain this answer?
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The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).a)9 : 16b)9 : 25c)16 : 25d)16 : 27Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).a)9 : 16b)9 : 25c)16 : 25d)16 : 27Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. find the ratio of the area of the annular zone to the area of the larger circle. (Area of the annular zone is the difference between the area of the larger circle and that of the smaller circle).a)9 : 16b)9 : 25c)16 : 25d)16 : 27Correct answer is option 'C'. Can you explain this answer?.
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