Chapter 12.5, Problem 13PSB

To determine

To calculate: The total volume of gazebo with a pentagonal base area of $60m^2$ .

Answer to Problem 13PSB

The total volume of gazebo is $720m^3$ .

Explanation of Solution

Given information:

Pentagonal base area $=60m^2$ ,

Total height = 16 m,

Pyramid height = 6 m.

Formula used:

Volume of prism $=B\times h$

B = Base area of prism and h = height of prism

Volume of pyramid $=\frac{1}{3}\times B\times h$

B = Base area of pyramid and h = height of pyramid

Calculation:

  

Volume of prism $=B\times h$

  $B=$ Pentagonal base area $=60m^2$ .

Prism height = Total height − Pyramid height

Prism height $=16-6=10m$

Volume of prism $=60\times 10$

Volume of prism $=600m^3$

Volume of pyramid:

  $B=$ Pentagonal base area $=60m^2$ .

Pyramid height = 6 m.

  $\begin{array}{l}{V}_{Pyramid}=\frac{1}{3}\times B\times h\\ V_{Pyramid}=\frac{1}{3}\times 60\times 6\\ V_{Pyramid}=120m^3\end{array}$

Total Volume = Volume of prism + Volume of pyramid

Total Volume $=600+120$

Total Volume $=720m^3$