Question

What is the area of the shaded sector? 6Pi units squared 9Pi units squared 18Pi units squared 36Pi units squared

Answer 1

The area of the sector with a central angle of
`\((\pi)/(2)\)` radians and a radius of 6 units is 9 pi square units. The correct option is B.

The formula for the area
`(\(A_{\text{sector}}\))` of a sector of a circle is given by:

`\[ A_{\text{sector}} = (\theta)/(2) \cdot r^2 \]`

where:

-
`\(\theta\)` is the measure of the central angle in radians,

- r is the radius of the circle.

In this case,
`\(\theta = (\pi)/(2)\)` (as given) and r = 6. Substitute these values into the formula:

`\[ A_{\text{sector}} = ((\pi)/(2))/(2) \cdot 6^2 \]\[ A_{\text{sector}} = (\pi)/(4) \cdot 36 \]\[ A_{\text{sector}} = 9\pi \]`

So, the area of the sector is 9 pi square units. Therefore, the correct answer is 9 pi units squared.

Option B is correct.

Question:

What is the area of the shaded sector?

A. 6Pi units squared

B. 9Pi units squared

C. 18Pi units squared

D. 36Pi units squared