Question

Answer and Explain how to do both questions

Answer 1

a) Area of sector TRV =
`42.4\: units^2`

b)
`0.8\: units`

Explanation:

a)

In
`\odot R`, TW is diameter.

Therefore,

`m\widehat {TVW} = 180\degree`

`\because m\widehat {TV} +m\widehat {VW} =m\widehat {TVW}`

`\therefore m\widehat {TV} +120\degree =180\degree`

`\therefore m\widehat {TV} =180\degree - 120\degree`

`\therefore m\widehat {TV} = 60\degree`

`\because m\angle TRV=m\widehat{TV}`

(Measure of central angle is equal to the measure of its corresponding arc)

`\therefore m\angle TRV\:(\theta) =60\degree`

Radius (r) = RW = 9 units

Area of sector TRV

`=(\theta)/(360\degree)* \pi r^2`

`=(60\degree)/(360\degree) * 3.14* 9^2`

`=(1)/(6) * 3.14* 81`

`=(1)/(6) * 254.34`

`=42.39\: units^2`

Area of sector TRV
`=42.4\:units^2`

b)

Length of
`\widehat{VW}`

`=(120\degree )/(360\degree) * 2\pi r`

`=(2)/(3) * 3.14* 9`

`=2 * 3.14* 3`

Length of
`\widehat{VW}`
`= 18.84\: units`

`\overline{TW} =2*RW =2*9 = 18\: units`

`\widehat{VW}- \overline{TW}= 18.84-18=0.84\: units`

`\widehat{VW}- \overline{TW}= 0.8\: units`