Question

What is the approximate area of the shaded sector in the circle shown below? 

Answer 1

Answer

4.71 cm²

Explanation

Area of a circle = πr²

Where r is the radius of the circle.

For a sector which is  part of a circle, its area is given by;

Area of a sector = (Ф/360)πr²

where Ф is the angle making the sector at the center of the circle.

∴ Area of a sector = (Ф/360)πr²

                             = 60/360 × π × 3²

                             = 1/6 × π × 9

                              = 4.71 cm²

Answer 2

The area of shaded sector is $\boxed{4.71{\text{ c}}{{\text{m}}^2}}.$

Further explanation:

The formula for area of sector can be expressed as follows,

$\boxed{{\text{Area of sector}} = \frac{\theta }{{{{360}^ \circ }}} \times \pi {r^2}}$

Here, $\theta$ is the central angle and r is the radius of the circle.

Given:

The radius of the circle is $3{\text{ cm}}.$

The central angle is ${60^ \circ }.$

Explanation:

The radius of the sector is $3{\text{ cm}}$ and the angle is $\theta = {60^ \circ }.$

The area of shaded sector can be calculated as follows,

$\begin{aligned}{\text{Area of sector}}&= \frac{\theta }{{360}} \times \pi {r^2}\\&= \frac{{60}}{{360}} \times \frac{{22}}{7} \times {\left( 3 \right)^2}\\&= \frac{1}{6} \times \frac{{22}}{7} \times 9\\&= \frac{{22 \times 9}}{{6 \times 7}}\\\end{aligned}$

Further solve the above equation.

$\begin{aligned}{\text{Area of sector}} &= \frac{{198}}{{42}}\\&= 4.71{\text{ c}}{{\text{m}}^2}\\\end{aligned}$

The area of shaded sector is $\boxed{4.71{\text{ c}}{{\text{m}}^2}}.$

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Circles

Keywords: Radius of circle, arc length, radian, central angle, intercepted, circle, circumference, sector of a circle, minor sector, major sector, segment, angle.