Question

If sector of a circle has an area of 40π sq units and a central angle of 72°, the radius of the circle is ______.

Options

• 200 units

• 100 units

• 20 units

• `10sqrt2` units

Answer 1

If sector of a circle has an area of 40π sq units and a central angle of 72°, the radius of the circle is `bbunderline(10sqrt2  units)`.

Explanation:

Given:

A = 40π sq units.

θ = 72°

r = ?

Formula:

A = `θ/(360°) xx pir^2`

Calculation:

Substitute the values into the formula

⇒ `40π = 72/360 xx pir^2`

⇒ `40π = 1/5 xx pir^2`

⇒ r² = 40 × 5

⇒ r² = 200

⇒ `r = sqrt200`

⇒ `r = sqrt(100 xx 2)`

⇒ r = `10sqrt2` units.