Question

ross is trying to remember the formula for the volume of a cylinder. he knows that the volume of a prism or cylinder can be calculated as ( v = bh ), where ( b ) is the area of the base and ( h ) is the height. which two additional pieces of information does ross need to explain the formula ( v=pi r^{2}h ) for the volume of a cylinder? the circumference of a circle is ( 2pi r ). the area of a circle is ( pi r^{2} ). the base of a cylinder is a circle. the curved surface of a cylinder can be formed by wrapping a rectangle around two circles.

Explanation:

Since the volume formula for a prism/cylinder is \(V = Bh\), for a cylinder, we need to know that the base \(B\) is a circle (so we can use the area formula for a circle). The area formula of a circle is \(A=\pi r^{2}\). Substituting \(B = \pi r^{2}\) into \(V=Bh\) gives \(V=\pi r^{2}h\). The circumference of a circle (\(C = 2\pi r\)) is related to the lateral surface area of a cylinder (\(S=Ch\)) but not directly to the volume formula derivation here. The fact about the curved - surface (while true) is more relevant to surface - area discussions.

Answer:

• The area of a circle is \(\pi r^{2}\).
• The base of a cylinder is a circle.