Answer:
=
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
y + 2x = 2 ( subtract 2x from both sides )
y = - 2x + 2 ← in slope- intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
= -
= -
=
I assume the base of S is the disk centered at the origin, or x² + y² ≤ r². Solving for y gives two solutions corresponding to the upper and lower halves of the circular boundary,
and the vertical distance between them - i.e. the side length of each cross section - is
Then the volume of each square cross section 4 (r² - x²) ∆x, and the volume of S is
By symmetry, this is the same as
which gives a volume of