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If the radius of a circle is increased by 5%, find the percentage increase in its area.
- a)10%
- b)10.25%
- c)10.75%
- d)11%
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the radius of a circle is increased by 5%, find the percentage incr...
% increase in its area
= 2 × 5 + 52/100
= 10 + 0.25 =10.25%
= 2 × 5 + 52/100
= 10 + 0.25 =10.25%
Most Upvoted Answer
If the radius of a circle is increased by 5%, find the percentage incr...
To find the percentage increase in the area of a circle when its radius is increased by 5%, we can follow these steps:
1. Calculate the original area of the circle:
- The formula for the area of a circle is A = πr², where A is the area and r is the radius.
- Let's assume the original radius of the circle is 'r'.
- So, the original area, A1 = πr².
2. Calculate the new radius of the circle after it is increased by 5%:
- The new radius can be calculated by adding 5% of the original radius to the original radius.
- 5% of the original radius = (5/100) * r = 0.05r
- Therefore, the new radius, r2 = r + 0.05r = 1.05r.
3. Calculate the new area of the circle:
- Using the formula for the area of the circle, A2 = π(1.05r)² = π(1.1025r²).
4. Find the percentage increase in the area:
- The percentage increase can be calculated using the formula:
Percentage increase = ((new value - original value) / original value) * 100
- Substituting the values, we get:
Percentage increase = ((A2 - A1) / A1) * 100
= ((π(1.1025r²) - πr²) / πr²) * 100
= (0.1025) * 100
= 10.25%
Therefore, the percentage increase in the area of the circle when its radius is increased by 5% is 10.25%. Hence, the correct answer is option 'B' - 10.25%.
1. Calculate the original area of the circle:
- The formula for the area of a circle is A = πr², where A is the area and r is the radius.
- Let's assume the original radius of the circle is 'r'.
- So, the original area, A1 = πr².
2. Calculate the new radius of the circle after it is increased by 5%:
- The new radius can be calculated by adding 5% of the original radius to the original radius.
- 5% of the original radius = (5/100) * r = 0.05r
- Therefore, the new radius, r2 = r + 0.05r = 1.05r.
3. Calculate the new area of the circle:
- Using the formula for the area of the circle, A2 = π(1.05r)² = π(1.1025r²).
4. Find the percentage increase in the area:
- The percentage increase can be calculated using the formula:
Percentage increase = ((new value - original value) / original value) * 100
- Substituting the values, we get:
Percentage increase = ((A2 - A1) / A1) * 100
= ((π(1.1025r²) - πr²) / πr²) * 100
= (0.1025) * 100
= 10.25%
Therefore, the percentage increase in the area of the circle when its radius is increased by 5% is 10.25%. Hence, the correct answer is option 'B' - 10.25%.
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