Question

Find the volume and surface area of the right prism. Round your answer to twodecimal places, if necessary.

Answer 1

The given diagram represents a prism whose cross-sectional area of base is an equilateral triangle with side 10 yd, and the height of the prism is 8 yd.

The total surface area of the prism will be the sum of the area of its faces.

There are 3 identical rectangular faces and 2 identical triangular faces in the prism.

Then the surface area of the prism is calculated as,

`\begin{gathered} SA=3\cdot(A_(rect))+2\cdot(A_(triangle)) \\ SA=3\cdot(8*10)+2\cdot(\frac{\sqrt[]{3}}{4}*10^2) \\ SA=240+50\sqrt[]{3} \\ SA\approx326.60 \end{gathered}`

So the surface area of the given prism is 326.60 sq. yd. approximately.

Consider that the prism has the equilateral triangular section throughout its length.

So the volume (V) is given by,

`\begin{gathered} V=A_(triangle)* Height \\ V=(\frac{\sqrt[]{3}}{4}*10^2)*8 \\ V=200\sqrt[]{3} \\ V\approx346.41 \end{gathered}`

Thus, the volume of the given prism is 346.41 cu. yd. approximately.