Question

I need help with a problem

Answer 1

step 1

Find out the area of the circle

`A=\pi\cdot r^2`

where

r=4 units

substitute

`\begin{gathered} A=\pi\cdot4^2 \\ A=16\pi\text{ unit2} \end{gathered}`

step 2

Find out the area of the sector

Remember that

The area of the complete circle subtends a central angle of 2pi radians

so

Applying proportion

Find out the area of the sector by a central angle of 2pi/3 radians

16pi/2pi=x/(2pi/3)

solve for x

x=8*(2pi/3)

x=16pi/3 unit2

the area of the sector is 16pi/3 unit2

step 3

Find out the circumference of the circle

`\begin{gathered} C=2\pi r \\ C=2\pi\cdot(4) \\ C=8\pi\text{ unit} \end{gathered}`

step 4

Find out the arc length by a central angle of 2pi/3 radians

Remember that

The circumference of the circle subtends a central angle of 2pi radians

so

Applying proportion

8pi/2pi=x/(2pi/3)

x=4*(2pi/3)

x=8pi/3 units

therefore

Verify each statement

N 1 -----> false

N 2 ----> true

N 3 ---> true