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romanna [79]
4 years ago
5

use the formula for the circumference of a circle to write a formula for the area of a circle in terms of its circumference

Mathematics
1 answer:
Ber [7]4 years ago
6 0

Answer:

A=\frac{C^2}{4\pi ^2}

Step-by-step explanation:

Recall to find the circumference of a circle the formula is C=\pi d or C=2\pi r. We will also need the formula for the area of a circle which is A=\pi r^{2}. Since the area formula is in terms of r we will use the second formula for circumference.

We start by solving for r in the Circumference formula.

C=2\pi r\\\frac{C}{2\pi } =r. We input this value of r into the area formula.

A=\pi r^{2} \\A=\pi (\frac{C}{2\pi })^2\\A=\pi (\frac{C^2}{4\pi ^2 })\\A=\frac{C^2}{4\pi ^2}

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