An arc ofa circle is of length 7n em and the sector it bounds has an area of 28t cm?. Find the radius of the circle.

1 thought on “An arc ofa circle is of length 7n em and the sector it bounds has an area of 28t cm?. Find the radius of the circle.”

1. Step-by-step explanation:

   Arc of circle of length = 7π cm.

   [tex]sector \: it \: bounds \: has \: an \: area \: = 28\pi \: {cm}^{2}.[/tex]

   Radius of circle = ?

   We know that

   [tex]length \: of \: an \: arc \: of \: circle \: \frac{2\pi r θ }{360 {}^{0} } [/tex]

   Therefore,

   [tex]7\pi \ = \frac{2\pi r θ }{ {360}^{0} } [/tex]

   [tex]r θ = {180}^{0} \times 7[/tex]

   [tex]θ = \frac{1260}{r}…. (1) [/tex]

   And

   [tex]area \: of \: sector \: = \frac{\pi \: r {}^{2} θ}{ {360}^{0} }

   [/tex]

   [tex]28\pi \times \frac{\pi \: r^{2} θ}{ {360}^{0} } [/tex]

   [tex] {r}^{2} θ \: = 28 \times {360}^{0} [/tex]

   [tex]θ = \frac{28 \times {360}^{0} }{ {r}^{2} } ….(2)[/tex]

   From (1) and (2) to and we get,

   [tex] \frac{1260}{r} = \frac{28 \times 360 {}^{0} }{ {r}^{2} } [/tex]

   [tex]r \times \frac{28 \times {360}^{0} }{1260} [/tex]

   [tex]r \: = 8c.m[/tex]

   Hence, this is the answer

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