Question

An arc of a circle is of the length of 7 Pi cm and the sector bounds an area of 28 cm2.Find the radius.

Answer 1

28/11 is the radius of the circle which is of length 7 Pi cm and the sector bounds an area of 28 cm2

Answer 2

Answer:

The radius is  8/π cm.

Step-by-step explanation:

Given : An arc of a circle is of the length of 7π cm and the sector bounds an area of 28 cm square.

To find : The radius?

Solution :

Let the radius of the circle be 'r' cm.

Length of an arc of the circle = 7π cm and area of the sector = 28 cm²

We know that, length of an arc of the circle = θ(2πr)/360°

Therefore,

θ(2πr)/360° = 7π

⇒ θr = 180*7

⇒ θr = 1260

⇒ θ = 1260/r .........(1)

And,

Area of the sector = πr²θ/360°

Therefore,

πr²θ/360° = 28

⇒ πr²θ = 360*28

⇒ πr²θ = 10080 ...........(2)

Substitute value of θ from equation (1) in the equation (2), we get

⇒ πr²(1260/r) = 10080

⇒ πr = 10080/1260

⇒ πr = 8 cm

⇒ r = 8/π cm

Therefore, The radius is  8/π cm.