Answer:
The volume of the figure is equal to
or 
Step-by-step explanation:
we know that
The volume of the composite figure is equal to the volume of a cone plus the volume of a cylinder
step 1
Fin the volume of a cone
The volume of a cone is equal to

we have


substitute

step 2
Find the volume of the cylinder
The volume of the cylinder is equal to

we have


substitute

step 3
Find the volume of the figure

Convert to mixed number

F(x) as a piecewise function would be:
f(x) = ($3/lb)x, for 0≤x≤10,
= ($1.50/lb)x, for (10,20], and
= ($0.50/lb)x, for (20,40]
To the above must be added $7.50, [0,10] or $12, (10,40]
R = v/4
because:
v = 4r
v/4 = 4r/4 the fours cancel out and you are left with r
therefore v/4 = r or r = v/4