Volume of Prisms and Cylinders

A prism or cylinder is just one flat shape, the base, repeated over and over until it reaches some height. A cylinder is a stack of identical circles. A triangular prism is a stack of identical triangles. Since every layer has the same area, the total volume is simply base area times height: V = B times h. No separate formula to memorize for each shape, just two steps: find the area of the base, then multiply by the height.

This is why the test gives you no formula sheet for this topic but still expects correct answers. You already know area formulas: π r² for a circle, (1/2) base times height for a triangle, side² for a square. Volume of a prism or cylinder only asks you to apply one of those, then multiply once more. The hard part is rarely the volume rule itself; it's picking out the right base and the right height from a solid drawn at an angle, especially when a triangular prism lies on its side and the 'base' isn't the bottom face you'd point to first.

This connects directly to surface area, which comes next: surface area adds up the areas of every face, while volume multiplies one face's area through the depth. Keep those two operations straight — add for surface, multiply for volume — and both topics get much easier.