Question

?

The diameter of a circle is two times its radius. Which equation shows
another way to represent the area of a circle?
πd2
A=
2
O πd2
A=
4
Ο Α = 2πd?
O A=47d2

Answer 1

`A=\pi (d^2)/(4)`

Explanation:

The typical equation for the area of a circle is
`A=\pi r^2`. Since the answer choices are in terms of d, the diameter of the circle, you will need to find r in terms of d.

To find r in terms of d, you know that the diameter of a circle is two times its radius. As an equation, this is

`d=2r`, or solving for r,

`r = (d)/(2)`.

Now that you have an equation for r in terms of d, you can substitute r with
`(d)/(2)` from the original equation.

`A=\pi r^2`

`A=\pi ((d)/(2))^2`

`A=\pi (d^2)/(4)`