Question

A circle with area 36 has a sector with a central angle of 11/6pi
radians.
What is the area of the sector?

Answer 1

Answer:

33 sq. units

Step-by-step explanation:

The area of a sector can be calculated using the formula;

$A = \frac{ 1}{2} {r}^{2} \theta$

From the given information, the area of the circle is 36 and the angle of sector is

This means

$\pi {r}^{2} = 36 \\ {r}^{2} = \frac{36}{\pi}$

We substitute the values into the formula to get:

$A = \frac{ 1}{2} \times \frac{36}{\pi} \times \frac{11}{6} \pi$

We cancel out common factors to get:

$A =33$

The area of sector is 33 square units