Question 907364
The entire area of the pie is 
{{{A=pi*R^2=pi(12^2)=144pi}}}{{{cm^2}}}
.
.
.

a) Each slice is 40 degrees, the entire pie is 360 degrees, so,
{{{N=360/40=9}}}
.
.
b) Each slice is 1/9 the total area,
{{{A[s]=A/9=(144pi)/9=16pi}}}
.
.

c) The arc length of a circular sector is,
{{{S=R*theta}}}
where {{{theta}}} is in radians.
There are {{{2pi}}} radians in 360 degrees so,
{{{theta=40*((2pi)/360)}}}
{{{theta=(2/9)pi}}}
So,
{{{S=12*(2/9)pi}}}
{{{S=(8/3)pi}}}{{{cm}}}