Question

Find the area of the shaded sector. Leave your answer in terms of π.

48π m2

16π m2

32π m2

64π m2

Answer 1

Option 2. 16π m².

Explanation:

Area of a circle is represented as
`A = \pi r^(2)`

Then area of an arc having angle = ∅

A' = (∅/2π)×πr²

Now we have an arc having an angle ∅ = 90° and r = 8 m

Therefore Area of the arc = (90/360)×π×8²

= (1/4)×π×64

= 16 π m²

So 16 π m² is the right answer.

Answer 2

16π m2

Explanation:

The area of a sector (A) is given by:

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

Where

`\theta` is the angle of the sector

r is the radius of the circle

We can see that the angle of the sector is 90, and the radius of the circle is 8. Plugging these into the formula, we get:

`A=(90)/(360)* \pi (8)^2\\A=(1)/(4)* \pi (64)\\A=16 \pi`

The area is 16π m2