Question

What is the right answer to this? I calulated and it said the first option was wrong. Find the area of the sector use 3.14 for pi

Answer 1

A ≈ 84.8 units²

Explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

= πr² ×
`(120)/(360)`

= π × 9² ×
`(1)/(3)`

= 81π ×
`(1)/(3)`

= 27π

= 27 × 3.14

≈ 84.8 units² ( to the nearest tenth )

Answer 2

84.8

Explanation:

`\textsf{Area of a sector of a circle}=\left((\theta)/(360^(\circ))\right) \pi r^2`

`\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}`

Given:

• 
  `\theta` = 120°
• 
  `\pi` = 3.14
• r = 9

Substitute the given values into the formula:

`\begin{aligned}\implies \textsf{Area} & =\left((120^(\circ))/(360^(\circ))\right) \cdot 3.14 \cdot 9^2\\\\& = (1)/(3) \cdot 3.14 \cdot 81\\\\& = 84.78\\\\ & = 84.8\: \sf (nearest\:tenth)\end{aligned}`