Question

Hello! Can anyone assist me with this exercise? It will be appreciated.​

Answer 1

1) a) 4.28in b) 14.97in²

2) a) 39.09m b) 156.38m²

3) a) 25.92cm b) 142.55cm²

Explanation:

1. For the first scenario:

`\sf \theta = 35^\circ`,
`\sf r = 7 \, \textsf{in}`

Length of the arc:

`\sf \textsf{Length of arc} = (\theta)/(360^\circ) * 2\pi r`

`\sf \textsf{Length of arc} = (35)/(360) * 2\pi * 7`

`\sf \textsf{Length of arc} \approx 4.276056667 \, \textsf{in}`

`\sf \textsf{Length of arc} \approx 4.28 \, \textsf{in} \textsf{(in 2 d.p.)}`

Area of the arc:

`\sf \textsf{Area of the arc} = (\theta)/(360^\circ) * \pi r^2`

`\sf \textsf{Area of the arc} = (35)/(360) * \pi * 7^2`

`\sf \textsf{Area of the arc} \approx 14.96619834 \, \textsf{in}^2`

`\sf \textsf{Area of the arc} \approx 14.97 \, \textsf{in}^2 \textsf{(in 2 d.p.)}`

2. For the second scenario:

`\sf \theta = 280^\circ`,
`\sf r = 8 \, \textsf{m}`

Length of the arc:

`\sf \textsf{Length of arc} = (\theta)/(360^\circ) * 2\pi r`

`\sf \textsf{Length of arc} = (280)/(360) * 2\pi * 8`

`\sf \textsf{Length of arc} \approx 39.09537524 \, \textsf{m}`

`\sf \textsf{Length of arc} \approx 39.09 \, \textsf{m} \textsf{(in 2 d.p.)}`

Area of the arc:

`\sf \textsf{Area of the arc} = (\theta)/(360^\circ) * \pi r^2`

`\sf \textsf{Area of the arc} = (280)/(360) * \pi * 8^2`

`\sf \textsf{Area of the arc} \approx 156.381501 \, \textsf{m}^2`

`\sf \textsf{Area of the arc} \approx 156.38 \, \textsf{m}^2 \textsf{(in 2 d.p.)}`

3. For the third scenario:

`\sf \theta = 135^\circ`,
`\sf r = 11 \, \textsf{cm}`

Length of the arc:

`\sf \textsf{Length of arc} = (\theta)/(360^\circ) * 2\pi r`

`\sf \textsf{Length of arc} = (135)/(360) * 2\pi * 11`

`\sf \textsf{Length of arc} \approx 25.91813939 \, \textsf{cm}`

`\sf \textsf{Length of arc} \approx 25.92 \, \textsf{cm} \textsf{(in 2 d.p.)}`

Area of the arc:

`\sf \textsf{Area of the arc} = (\theta)/(360^\circ) * \pi r^2`

`\sf \textsf{Area of the arc} = (135)/(360) * \pi * 11^2`

`\sf \textsf{Area of the arc} \approx 142.5497667 \, \textsf{cm}^2`

`\sf \textsf{Area of the arc} \approx 142.55 \, \textsf{cm}^2 \textsf{(in 2 d.p.)}`