[ V = \int_c^d A(y) , dy ]
Common cross‑section shapes (when slices are perpendicular to the axis): volume by cross section practice problems pdf
| Shape | Area formula | |-------|---------------| | Square (side = (s)) | (A = s^2) | | Equilateral triangle (side = (s)) | (A = \frac\sqrt34 s^2) | | Right isosceles triangle (leg = (s)) | (A = \frac12 s^2) | | Semicircle (diameter = (s)) | (A = \frac\pi8 s^2) | | Rectangle (height = (h), base = (s)) | (A = h \cdot s) | [ V = \int_c^d A(y) , dy ]
Base: circle (x^2 + y^2 = 9). Cross sections perpendicular to the x‑axis are equilateral triangles. Find volume. [ V = \int_c^d A(y)