Chapter 12.5, Problem 18PSC

To determine

To calculate: The volume of octahedron which has an edge of $6$ .

Answer to Problem 18PSC

The volume of octahedron is $101.82$ .

Explanation of Solution

Given information:

  $e=6.$

Formula used:

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

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

Area of square: $A=s^2$

s = side of square

Calculation:

  

The octahedron can form two square pyramids; then

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

  $\begin{array}{l}B=s^2=6^2=36\\ h=3\sqrt{2}\end{array}$

Volume of pyramid $=\frac{1}{3}\times 36\times 3\sqrt{2}$

Volume of pyramid $=12\times 3\sqrt{2}=36\sqrt{2}=50.91$

Volume of two pyramid $=2\times 50.91=101.82$

Volume of octahedron = Volume of two pyramid $=72\sqrt{2}=101.82$