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

1056.25π square units

Step-by-step explanation:

A few formulas an definitions which will help us:

(1) , where c is the circumference of a circle and d is its diameter

(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) .

We can rearrange equation (1) to put d in terms of π and c, giving us (4) , 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:

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

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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step-by-step explanation:

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