Question

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the area of the sector given r = 4 cm and Θ =

π
3
.

A)
3π
4
cm2
B)
3π
8
cm2
C)
8π
3
cm2
D)
4π
3
cm2

Answer 1

c

Explanation:

4π

3

cm

First, find the radius

A = πr2 → r =

A

π

=

16π

π

= 4

If C = 2πr, then the arc length should equal the central angle, in radians, times the radius:

s = θr

s =

π

3

(4) =

4π

3

Answer 2

Your post is difficult to read. Please use " / " to denote division.

the length of an arc intercepted by an angle is proportional to the radius to find the area of the sector given r = 4 cm and Θ =
π
3
I will have to assume that your angle is pi/3.

The area of this circle is pi*r^2, or pi*(4 cm)^2, or 16*pi cm^2, and the area of the sector defined by pi/3 is

pi/3 (1/3)
-------- * 16*pi cm^2, or --------- * 16 pi cm^2, or (16 pi)/6 cm^2,
2pi 2

or 8pi/3 cm^2 (answer)