Question

The surface area, A, of a sphere in terms of its radius, r, is given by A(r) = 4πr2. Express r as a function of A.

Answer 1

r =√ ( A / 4π )

given A = 4πr² ( isolate r² by dividing both sides by 4π )

A / 4π = r² ( take the square root of both sides )

r =√( A / 4π )

Answer 2

The expression of r in terms of A is:

`r=\sqrt{(A)/(4\pi)}`

Explanation:

We are given the surface area, A, of a sphere in terms of its radius, r, as:

A(r) = 4πr²

`A=4\pi\ r^2`

⇒
`r^2=(A)/(4\pi)`

⇒
`r=\sqrt{(A)/(4\pi)}`

Hence, the expression of r in terms of A is:

`r=\sqrt{(A)/(4\pi)}`