Answer:
1056.25π square units
Step-by-step explanation:
A few formulas an definitions which will help us:
(1) [tex]\pi=\frac{c}{d}[/tex], where c is the circumference of a circle and d is its diameter
(2) [tex]A=\pi r^2[/tex], 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) [tex]d=2r \rightarrow r=\frac{d}{2}[/tex].
We can rearrange equation (1) to put d in terms of π and c, giving us (4) [tex]d = \frac{c}{\pi}[/tex], 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:
[tex]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}[/tex]
We can now substitute c for our circumference, 65, to get our answer in terms of π:
[tex]A=\dfrac{65^2}{4\pi}=\dfrac{4225}{4\pi}=1056.25\pi[/tex]
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
