Area of a circle as a function of the diameter? Need help quick!?

Question

How do you figure out the area of a circle as a function of the diameter? My AP Calc book says the answer it is pi x diameter squared/4 but I don't know how to get to that answer.

Answer 1

A = pi * (radius)^2

= pi* (diameter/2)^2

= pi * (diamater^2)/4

Answer 2

area = pi x r^2 where r is the radius

r = d/2

Area = pi x (d/2)^2

Area = pi x d^2/4 (when squaring a fraction you square both top and bottom of the fraction).

writing something as a function of something else means that it is determined by the value of it i.e if a = f(x) then the value of a is determined by the value of x. The thing it is a function of is always a variable.

Answer 3

Area = pi r^2

(where r=radius and r^2 = r squared)

and diameter, d, is 2r

d = 2r

divide both sides by 2, and you get

d/2 =r

or, r = d/2

substitute that into the equation at the top:

Area = pi (d/2)^2

Area = pi d^2/2^2

and we know that 2^2 = 2*2 = 4, so

Area = pi d^2/4 or

Area = pi x diameter squared/4

Answer 4

d=2r, r= d/2

Area = pi r^2 =pi(d/2)^2 = pi d /4

Answer 5

Area of a circle:

A = πr²

Diameter:

d = 2r

r = d/2

Just do a quick substitution:

A = π(d/2)²

A = πd² / 4

Answer 6

A = πr²

r = d/2

A = π(d/2)² = πd²/2² = πd²/4

Answer 7

Yes, it is (PI x D^2) / 4.

Or another way of thinking of this is using the radius (half the diameter) in (PI x R^2 ) / 2.