Question

The area (A) of a circle with a radius of r is given by the formula and its diameter (d) is given by . Arrange the equations in the correct sequence to rewrite the formula for diameter in terms of the area of the circle.

Answer 1

see explanation

Explanation:

A = πr² ← r is the radius and r =
`(1)/(2)` d ← d is the diameter

Hence

π (
`(1)/(2)` d)² = A, that is

`(d^2\pi )/(4)` = A ( multiply both sides by 4 )

d²π = 4A ( divide both sides by π )

d² =
`(4A)/(\pi )` ( take the square root of both sides )

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