Question

Explain the similarities and differences between volume formulas for prisms and cylinders.

Answer 1

Hint: A prism is solid with bases that are polygons and the sides are flat surfaces. A cylinder is not a prism, however, it is extremely similar. If a prism is imagined with regular polygons for bases as we increase the number of sides, the solid gets to look just like a cylinder. A cylinder is a prism with an infinite number of faces.

Complete step by step answer:
Prisms have two bases but pyramids only have one.
They are both similar in the way that the formula is base multiplied by the height. They are different because of the type of shape on the base.
The formula for any prism would be base \[x\]height. Whatever the base might be (a square, rectangle, pentagon, etc.).
For example, the volume of a rectangular prism can be given by,
\[
  A = B \times h \\
   \Rightarrow A = \left( {l \times w} \right) \times h \\
   \Rightarrow A = lwh \\
 \]
A cylinder is the same thing, base time’s height. But the base is a circle which is\[A = \pi {r^2}\].
So,
\[
  A = B \times h \\
   \Rightarrow A = \pi \times {r^2} \times h \\
 \]

Note:
 Neither prisms nor pyramids have rounded sides, rounded edges, or rounded angles, distinguishing them from cylinders and spheres. All of the side faces meet at the bases or at the base in the case of pyramids. The bases on pyramids and prisms differ. Prisms have two congruent or identical bases and pyramids only have one base. The shape of the base on pyramids and prisms can vary, depending on the shape of the overall three-dimensional object. The base could have any shape but it is never a circle or an oval on a prism or pyramid.