Question

Find the volume of the given prism. Round to the nearest tenth if necessary.A.2,511.5 yd^3B.1,255.7 yd^3C.1,025.3 yd^3D.1,450.0 yd^3

Answer 1

Given:

The sides of an equilateral triangle base are 10 yds. The height of the prism is 29 yds.

To find:

The volume of the prism.

Solution:

The formula of the volume of the triangular prism is given by:

`V=\text{ (area of base)}*\text{ (height of the prism)}`

It is known that the area of the equilateral triangle is given by:

`A=\frac{\sqrt[]{3}}{4}(side)^2`

So, the area of the base of the triangular prism is:

`\begin{gathered} A=\frac{\sqrt[]{3}}{4}(10)^2 \\ =(1.732)/(4)*100 \\ =(173.2)/(4) \\ =43.30 \end{gathered}`

Now, the volume of the given triangular prism is:

`\begin{gathered} V=43.30*29 \\ =1255.7\text{ yad\textasciicircum{}3} \end{gathered}`