Question

What is the area of the sector shown in the diagram below?

Answer 1

`\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ -------\\ r=8\\ \theta = 40 \end{cases}\implies A=\cfrac{40\pi \cdot 8^2}{360}`

Answer 2

Option A is correct.

Explanation:

Given radius of the circle, r = 8 cm

Central Angle of the shaded Sector,
`\theta` = 40°

Area of Sector is given by the following formula,

`Area\:of\:Sector=(\theta)/(360^(\circ))*\pi r^2`

Putting given values we get,

Area of Sector =
`(40)/(360)*\pi(8)^2`

=
`(1)/(9)*3.14*64`

=
`22.3\:cm^2`

Therefore, Option A is correct.