Chapter 12.5, Problem 6PSA

To determine

To calculate: The total volume of a tower which has height of 24 m.

Answer to Problem 6PSA

The total volume of a tower is $533m^3$ .

Explanation of Solution

Given information:

Height of wall = 20 m,

Height of tower = 24 m,

Rectangular base area of pyramid B $=25m^2$

Formula used:

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

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

Calculation:

  

Height of wall: h₁ = 20

Volume of rectangular box $=B\times h_1$

Volume of rectangular box $=25\times 20$

Volume of rectangular box $=500$

We need height difference between tower and wall.

Let $h_2=24-20=4$

Volume of pyramid:

  $\begin{array}{l}{V}_{Pyramid}=\frac{1}{3}\times B\times h_2\\ V_{Pyramid}=\frac{1}{3}\times 25\times 4\\ V_{Pyramid}=\frac{100}{3}\end{array}$

Total Volume = Volume of rectangular box + Volume of pyramid

Total Volume $=500+\frac{100}{3}$

Total Volume $=\frac{1600}{3}$

Total Volume $=533m^3$