Question

Find the area of the shaded portion the one who answer first will get brainliest

Answer 1

Answer:

≈ 77 cm²

Step-by-step explanation:

The area of the shaded portion is calculated as

area of outer sector - area of inner sector

= (πR² - π r²) × $\frac{60}{360}$ ( R is the outer radius, r is the inner radius )

= (π × 14² - π × 7² ) × $\frac{1}{6}$

= (196π - 49π ) ÷ 6

= 147π ÷ 6

≈ 77 cm² ( nearest whole number )

Answer 2

Answer:

$A_s=76.97\ cm^2$

Step-by-step explanation:

Circular Sector

It's the portion of a circle enclosed by two radii and an arc. The area of a sector is calculated as follows:

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

Where r is the radius and θ is the central angle expressed in radians. The central angle will be converted to radians:

$\theta=60*\frac{\pi}{180}=1.0472\ rad$

The shaded region in the figure can be obtained by subtracting the smaller sector A2 area from the larger sector area A1:

$A_s=A_1-A_2$

The larger area is calculated with a radius of r1=14 cm:

$\displaystyle A_1=\frac {14^{2}*1.0472 }{2}$

$\displaystyle A_1=102.626\ cm^2$

The smaller area is calculated with r2=7 cm:

$\displaystyle A_2=\frac {7^{2}*1.0472 }{2}$

$\displaystyle A_2=25.656\ cm^2$

The shaded area is:

$A_s=102.626\ cm^2-25.656\ cm^2$

$\boxed{A_s=76.97\ cm^2}$