Question

Hey circle area 25 pi has a sector with a central angle of 9/10 pi radians

Answer 1

Given:

Area of a circle = 25 pi unit²

The central angle of a sector of the circle, θ = $\frac{9}{10}$ π radians

To find:

Area of the sector

Solution:

Let "r" be the radius of the given circle

We have the formula of the area of a circle as,

Area = πr²

We will now substitute the given value of the area of the circle in the formula to find the radius of the circle,

25π = πr²

⇒ r² = 25

⇒ r = $\sqrt{25}$

⇒ r = 5 units

We are given the central angle "θ" in terms of radians, so to find the area of the sector of the circle we will use the following formula,

Area of sector = ½ × r² × θ

We will now substitute the values of r = 5 units and θ =  $\frac{9}{10}$ π radians  in the formula to find the area of the sector of the given circle,

∴ Area of the sector,

= ½ × 5² × $\frac{9}{10}$ π

= ½ × 5 × 5 × $\frac{9}{10}$ π

= ½ × 5 × $\frac{9}{2}$ π

= $\frac{45}{4}$π unit² or 11.25π unit²

Thus, the area of the sector is $\frac{45}{4}$π unit² or 11.25π unit².

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