Question

Find the area of each Arc. Round your answer to the nearest tenth. Part 2. NO LINKS!!​

Answer 1

#1

• Ø=75×π/180=5π/12

Area

• 1/2r²Ø
• 1/2(16)²(5π/12)
• 256/2(5π/12)
• 128(5π/12)
• 167.4m²

#2

Area

• 1/2(14)²(19π/12)
• 196/2(19π/12)
• 98(19π/12)
• 487.2ft²

Answer 2

• 167.61 m²
• 487.66 ft.²

Explanation:

6) We would like to find out the area of the following arcs with ,

• radius = 16 m
• 
  `\theta` = 75° .

As we know that the area of sector is given by ,

`\longrightarrow Area =(\theta)/(360^o)* \pi r^2`

Here on substituting the respective values , we have ,

`\longrightarrow Area =(75)/(360)* (22)/(7)* 16m * 16m \\`

Simplify,

`\longrightarrow \underline{\underline{Area =167.61 \ m^2}}`

8) Again we would like to find out the area with ,

• r = 14ft
• 
  `\theta` = 19π/12 rad.

Firstly we know that ,

`\longrightarrow \pi \ rad = 180^o`

So ,

`\longrightarrow 2\pi rad = 360^o`

Therefore , the formula becomes ,

`\longrightarrow Area =(\theta)/(2\pi)* πr^2`

Substitute ,

`\longrightarrow Area =(19\pi)/(12* 2\pi)* \pi r^2\\`

So that,

`\longrightarrow Area =(19)/(24)* (22)/(7)* 14ft * 14ft \\`

Simplify,

`\longrightarrow \underline{\underline{ Area = 487.66 ft^2 }}`

And we are done !