Volume By Cross Section Practice Problems | Pdf

Common cross‑section shapes (when slices are perpendicular to the axis):

Base: circle (x^2 + y^2 = 9). Cross sections perpendicular to the x‑axis are equilateral triangles. Find volume. volume by cross section practice problems pdf

Base: region between (y = 1) and (y = \cos x) from (x=-\pi/2) to (\pi/2). Cross sections perpendicular to the x‑axis are rectangles of height 3. Find volume. (y = 0)

Base: region bounded by (y = \sin x), (y = 0), (x=0), (x=\pi). Cross sections perpendicular to the x‑axis are semicircles (diameter in base). Find volume. volume by cross section practice problems pdf

[ V = \int_a^b A(x) , dx ]