Question

A circle with area 36 pi has a sector with a central angle of 11/6 pi radians what is the area of the cector

Answer 1

Answer:

The area of the sector is 33$\pi$.

Explanation:

A sector is a part of a circle that is formed by two radii (which forms a central angle), and an arc. The area of a sector (in radians) is given by:

                          = (θ ÷ $2\pi$) × $\pi r^{2}$

where: θ is the central angle of the sector and r is the radius of the circle of which the sector is a part.

Area of a circle = $\pi r^{2}$. But the area of the circles was given to be 36$\pi$.

Area of the sector = (θ ÷ $2\pi$) × area of the circle

                              = (θ ÷ $2\pi$) ×36$\pi$

θ has been given to be $\frac{11}{6}$$\pi$.

Therefore;

   Area of the sector = ($\frac{11}{6}$$\pi$ ÷ $2\pi$) ×36$\pi$

                                   = $\frac{11}{12}$ × 36$\pi$

                                   = 11 × 3$\pi$

                                   = 33$\pi$

The area of the sector is 33$\pi$.

Answer 2

Answer:33pi

Explanation: