Question

If sector area of the shaded circle garden is 8π, and radius of the circle garden is 8 inch. Below figure represent the given scenario, then find measurement of the central angle AOB

Answer 1

The measurement of the central angle AOB is 45 degrees

Explanation:

To solve this problem, we will have to work with fractions.

We will get the fraction of area the shaded portion is when compared to the whole garden.

First of all, we will need to calculate the area of the garden which is
`\pi r^(2)`

in this case, our radius is 8 inches.

Next, we will compare the area of the sector to the area of the garden. This will be

This will be the shaded area/ area of the whole garden

=
`(8\pi)/(\pi8^(2))`

`=(1)/(8)`

We will now convert this ratio to an angle by multiplying it by 360 degrees.

This will be:

`(1)/(8)* 360 = 45 degrees`

The measurement of the central angle AOB is 45 degrees