Chapter 12.5, Problem 1PSA

To determine

To calculate: The volume of a pyramid whose base is 14 and height is 30.

Answer to Problem 1PSA

The volume of a pyramid is $848.70$ .

Explanation of Solution

Given information:

Base of pyramid = 14,

Height of pyramid h = 30,

Sides of equilateral triangle s = 14.

Formula used:

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

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

Area of equilateral triangle: $A=\frac{s^2}{4}\sqrt{3}$

s = side of equilateral triangle

Calculation:

  

  $\begin{array}{l}B=A_{EquilateralTriangle}=\frac{{\left(14\right)}^2}{4}\sqrt{3}\\ B=A_{EquilateralTriangle}=49\sqrt{3}\end{array}$

  $\begin{array}{l}{V}_{Pyramid}=\frac{1}{3}\times B\times h\\ V_{Pyramid}=\frac{1}{3}\times 49\sqrt{3}\times 30\\ V_{Pyramid}=49\sqrt{3}\times 10\\ V_{Pyramid}=490\sqrt{3}\\ V_{Pyramid}=848.70\end{array}$