If the circumference is reduced by a factor of 6, then how many times will the area of the corresponding circle decrease?
| April 1, 2021 | education
The circumference is: C = 2 * π * R.
Then R = С / 2 * π.
The area of the circle is: S = π * R ^ 2 = π * C ^ 2/4 * π ^ 2 = C ^ 2/4 * π.
If we reduce the circumference by a factor of 6, C1 = (C / 6), then C1 ^ 2 = C ^ 2/36, hence the area of the circle will decrease 36 times.
Answer: The area of the circle will decrease 36 times.
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