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MrRissso [65]
3 years ago
10

The circumference of a circle is 65?. In terms of pi, what is the area of the circle?

Mathematics
2 answers:
iVinArrow [24]3 years ago
8 0

Answer:

1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) \pi=\frac{c}{d}, where c is the circumference of a circle and d is its diameter

(2) A=\pi r^2, where A is the area of a circle with radius r. To put it in terms of d, remember that a circle's diameter is simply twice its radius, or mathematically, (3) d=2r \rightarrow r=\frac{d}{2}.

We can rearrange equation (1) to put d in terms of π and c, giving us (4) d = \frac{c}{\pi}, and we can make a few substitutions in (2) using (3) and (4) to get use the area in terms of the circumference and π:

A=\pi r^2\\=\pi\left(\frac{d}{2}\right)^2\\=\pi\left(\frac{d^2}{4}\right)\\=\pi\left(\frac{(c/\pi)^2}{4}\right)\\=\pi\left(\frac{c^2/\pi^2}{4}\right)\\=\pi\left(\frac{c^2}{4\pi^2}\right)\\\\=\frac{\pi c^2}{4\pi^2}\\ =\frac{c^2}{4\pi}

We can now substitute c for our circumference, 65, to get our answer in terms of π:

A=\dfrac{65^2}{4\pi}=\dfrac{4225}{4\pi}=1056.25\pi

Verdich [7]3 years ago
5 0

Answer:

Area = 2112.5 / pi

Step-by-step explanation:

They are asking you not to use 3.14 for pi. Just leave it as a symbol.

C = 2*pi*r

C = 65

65 = 2*pi*r

65/(2*pi) = r

The area of a circle is 2*pi * r^2

Area = 2 * pi * (65/2pi)^2

Area = 2 * pi * 65^2/(4*pi^2)           Cancel out one of the pi-s in the denominator

Area = 2 * 65^2 / (4 * Pi)                  Expand the numerator

Area = 8450/(4*pi)                           Divide by 4

Area = 2112.5 / pi

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