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If diameter of a circle is increased by 12%, find the percentage increase in its circumference.
- a)6%
- b)12%
- c)18%
- d)9%
Correct answer is option 'B'. Can you explain this answer?
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If diameter of a circle is increased by 12%, find the percentage incre...
Diameter is rarely used as the measuring side of a circle. Thus % increase in circumference =12%
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If diameter of a circle is increased by 12%, find the percentage incre...
Question:
If the diameter of a circle is increased by 12%, find the percentage increase in its circumference.
Answer:
To find the percentage increase in the circumference of a circle when its diameter is increased by 12%, we can follow the steps below:
1. Understanding the relationship between diameter and circumference:
- The diameter of a circle is the distance across the circle passing through its center.
- The circumference of a circle is the distance around the circle.
- The circumference of a circle can be calculated using the formula: C = πd, where C is the circumference and d is the diameter.
2. Calculating the original circumference:
- Let's assume the original diameter of the circle is d.
- The original circumference of the circle can be calculated using the formula C = πd.
3. Calculating the new diameter:
- When the diameter is increased by 12%, the new diameter becomes d + 0.12d = 1.12d.
4. Calculating the new circumference:
- The new circumference of the circle can be calculated using the formula C = π(1.12d).
5. Calculating the percentage increase:
- The percentage increase in the circumference can be calculated using the formula: (New Value - Original Value) / Original Value * 100.
- Substitute the values into the formula: ((π(1.12d) - πd) / πd) * 100.
Simplifying the expression: ((1.12 - 1) / 1) * 100 = 0.12 * 100 = 12%.
Therefore, the percentage increase in the circumference of the circle when its diameter is increased by 12% is 12%. The correct answer is option 'B'.
If the diameter of a circle is increased by 12%, find the percentage increase in its circumference.
Answer:
To find the percentage increase in the circumference of a circle when its diameter is increased by 12%, we can follow the steps below:
1. Understanding the relationship between diameter and circumference:
- The diameter of a circle is the distance across the circle passing through its center.
- The circumference of a circle is the distance around the circle.
- The circumference of a circle can be calculated using the formula: C = πd, where C is the circumference and d is the diameter.
2. Calculating the original circumference:
- Let's assume the original diameter of the circle is d.
- The original circumference of the circle can be calculated using the formula C = πd.
3. Calculating the new diameter:
- When the diameter is increased by 12%, the new diameter becomes d + 0.12d = 1.12d.
4. Calculating the new circumference:
- The new circumference of the circle can be calculated using the formula C = π(1.12d).
5. Calculating the percentage increase:
- The percentage increase in the circumference can be calculated using the formula: (New Value - Original Value) / Original Value * 100.
- Substitute the values into the formula: ((π(1.12d) - πd) / πd) * 100.
Simplifying the expression: ((1.12 - 1) / 1) * 100 = 0.12 * 100 = 12%.
Therefore, the percentage increase in the circumference of the circle when its diameter is increased by 12% is 12%. The correct answer is option 'B'.
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If diameter of a circle is increased by 12%, find the percentage increase in its circumference.a)6%b)12%c)18%d)9%Correct answer is option 'B'. Can you explain this answer?
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