Question

An arc measures 50°in a circle with a radius of 8 cm. What is the area of the sector to the nearest tenth of a square centimeter?

a.57.6m(squared)
b. 27.9m (squared)
c. 175m(squared)
d.7.0cm(squared)

Answer 1

`27.9cm^2`

Explanation:

The total area of the circle is given by:

`a=\pi r^2`

where
`\pi` is a constant
`\pi=3.1416`

and
`r` is the radius:
`r=8cm`

Thus the total area of this circle is:

`a=(3.1416)(8cm)^2\\a=(3.1416)(64cm^2)\\a=201.06cm^2`

We want only the area of the arc that measures 50°. For this we must remember that the arc of the total circle is 360°.

Thus, we want 50° out of the 360° degrees in the circle. For this, we divide the total area by 360 and then we multiply by 50:

`(201.06cm^2)/(360)(50)=0.5585cm^2(50)=27.9cm^2`

the area of the sector to the nearest tenth is
`27.9cm^2`