Question

The pentagonal prism below has a base area of 39.1 units^2 and a volume of 273.7 units^3. Find its height.

Answer 1

The base area of a pentagonal prism is given as 39.1 square units and its volume is given as 273.7 cubic units. It is required to find the height.

Recall that the volume of a prism with base area B and height h is given as:

`V=B\cdot h`

Substitute V=273.7 and B=39.1 into the formula and solve for h:

`\begin{gathered} 273.7=39.1\cdot h \\ \text{ Divide both sides by }39.1: \\ \Rightarrow(273.7)/(39.1)=(39.1\cdot h)/(39.1) \\ \Rightarrow7=h \end{gathered}`

Hence, the height of the pentagonal prism is h=7 units.

The height is h=7 units.