QUESTION 34 Find the exact area of the sector of a circle with radius 3 units and subtended angle of $$ 60^{\circ} $$.

Question

UpStudy AI · Accepted Answer

To find the area of a sector of a circle, we can use the formula:

$$
A = \frac{\theta}{360} \times \pi r^2
$$

where:
- $$ A $$ is the area of the sector,
- $$ \theta $$ is the angle in degrees,
- $$ r $$ is the radius of the circle.

Given:
- $$ r = 3 $$ units,
- $$ \theta = 60^{\circ} $$.

Now, we can substitute the known values into the formula:

$$
A = \frac{60}{360} \times \pi \times (3)^2
$$

Let's calculate this step by step.

1. Calculate $$ \frac{60}{360} $$:
   $$
   \frac{60}{360} = \frac{1}{6}
   $$

2. Calculate $$ (3)^2 $$:
   $$
   (3)^2 = 9
   $$

3. Substitute these values back into the area formula:
   $$
   A = \frac{1}{6} \times \pi \times 9
   $$

4. Simplify the expression:
   $$
   A = \frac{9\pi}{6} = \frac{3\pi}{2}
   $$

Thus, the exact area of the sector is:

$$
\frac{3\pi}{2} \text{ square units}
$$
The area of the sector is $$ \frac{3\pi}{2} $$ square units.

QUESTION 34 Find the exact area of the sector of a circle with radius 3 units and subtended angle of \( 60^{\circ} \).