Question

The circumference of a circle is 147 feet.
Find the area of the circle, in terms of pi.

Answer 1

Explanation:

C = 147 ft. The relevant formula is C = 2(pi)r, and here C = 147 ft = 2(pi)r.

The relevant area formula is A = (pi)r^2. If we solve the above formula for r we get

147 ft

r = ------------ and so r^2 (needed to calculate the area) is

2pi

147^2 ft^2

r^2 = ------------------

4(pi)

147^2 ft^2

and so the area is A = ---------------- = 7203/pi

3 pi

C C^2

Alternative method: C = 2pi*r so r = -------------- and r^2 = -------------

2 pi 4pi^2

C^2 C^2

then the area of the circle is A = pi(r^2) or pi*-------------- = ---------------

4pi^2 4pi

(147 ft)^2

and in this case the area of the circle is A = --------------

4 pi

or A = 1720 ft^2