Chapter 12.4, Problem 42HP

To determine

Tocalculate : The volume of equilateral triangle prism.

Answer to Problem 42HP

$V=\frac{80}{\sqrt{3}}uni{t}^3$

Explanation of Solution

Given information : An equilateral triangle prism with an apothem of 4 units and height of 5 units.

Formula used : The volume of equilateral triangle prism with the base area $B$ , apothem $a$ and height $h$ is $V=Bh$ . Where $B=\frac{a^2}{\sqrt{3}}$

Calculation : Calculate the base area of the equilateral triangle prism.

$\begin{array}{l}B=\frac{a^2}{\sqrt{3}}\\ =\frac{4^2}{\sqrt{3}}\\ B=\frac{16}{\sqrt{3}}uni{t}^2\end{array}$

Now, calculate the volume of the equilateral triangle prism.

$\begin{array}{l}V=Bh\\ =\frac{16}{\sqrt{3}}\times 5\\ V=\frac{80}{\sqrt{3}}uni{t}^3\end{array}$

Hence, the work of both is not correct.