Question

What is the diameter of circle T?

Answer 1

`Diameter = 16`

Explanation:

Given

`\theta = 72`

`Sector = (64)/(5)\pi`

Required

Calculate the diameter

The area of a sector is:

`Area = (\theta)/(360) * \pi r^2`

Substitute values for Area and
`\theta`

`(64)/(5)\pi = (72)/(360) * \pi r^2`

Divide both sides by
`\pi`

`(64)/(5) = (72)/(360) * r^2`

Make
`r^2` the subject

`(64*360)/(5*72) = r^2`

`(64*360)/(360) = r^2`

`64 = r^2`

Take positive square roots of both sides

`√(64) = r`

`8 = r`

`r = 8`

The diameter is then calculated as:

`Diameter = 2r`

`Diameter = 2*8`

`Diameter = 16`