Question

A circle with radius 6 has a sector with a central angle of 11/6 pi radians

Answer 1

Given:

The radius of a circle, r = 6 units

The central angle of a sector of the circle, θ = $\frac{11}{6}$π radians

To find:

Area of the sector

Solution:

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 given values of r and θ in the formula to find the area of the sector of the given circle,

Area = ½ × 6² × $\frac{11}{6}$π = ½ × 6 × 6 × $\frac{11}{6}$π = 3 × 11 π = 33π unit²

Thus, the area of the sector is 33π unit².

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