Question

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

Answer 1

Answer:

by means of radius it is π×r2

in terms of diameter it is (π×d2)÷4

in terms of circumference it is (circumference×r)÷2

Answer 2

$\bold{ A(r) = \pi r^2\\\\A(d) = \dfrac{\pi d^2}{4}\\\\A(C)=\dfrac{C^2}{4\pi}}$

Step-by-step explanation:

We have to express the area of circle.

Let r be the radius of circle, d be the diameter of circle and C be the circumference of circle.

(a) radius r

$\text{Area of circle}\\A(r) = \pi r^2$

(b) diameter d

$d = 2r\\\\r = \dfrac{d}{2}\\A(r) = \pi r^2\\A(d) = \pi (\dfrac{d}{2})^2\\\\A(d) = \dfrac{\pi d^2}{4}$

(c) circumference C.​

$C = 2\pi r\\\\r = \dfrac{C}{2\pi}\\\\A(r) = \pi r^2\\\\A(C) = \pi(\dfrac{C}{2\pi})^2 = \dfrac{\pi C^2}{4\pi^2} = \dfrac{C^2}{4\pi}$

#LearnMore

The circumference of a circle is C.which expression gives the area of the circle

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