Question

Sketch the region bounded by the following curves and find the volume of the solid generated by revolving this region about the x-axis.
x+y=1
x=0
10x+y=10

Answer 1

first you should start by solving those equations for y

\[y = 1 - x\]
\[x = 0\]
\[y = -10x + 10\]

and then graph them

Answer 2

the shaded area is the area you are going to revolve around the x axis.
Here, we need to find the points of intersection

which come out to be (0,1) (0,10) and (1, 0)