Express the area A of a circle as a function of its
(a) radius r
(b) diameter d
(c) circumference C.

Solution:

Let us consider a circle of radius r, diameter d

We know that the formula for the area of s circle is given by

Area = πr²

Let us express the area as a function of its radius, diameter, and circumference.

We know that the radius of a circle is half of its diameter

Then d/2 = r ⇒ d = 2r

We can rewrite the equation for the area as

A = π(d/2)²

A= πd²/4

The circumference of a circle with radius as r is given as 2πr

C = 2πr

⇒ r = C/2π

Area = πr²

Area = π. (C /2π)²

Multiply and divide to get in terms of circumference

Area = circumference² / 4π

A= C²/4π

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Express the area A of a circle as a function of its
(a) radius r
(b) diameter d
(c) circumference C.

Summary:

The area of a circle in terms of the radius is πr², in terms of its diameter is πd²/4 and in terms of its circumference is C²/ 4π