Chapter 12.3, Problem 4ST1

To determine

To find: the lateral surface area, total surface area and volume of a right hexagonal prism.

Answer to Problem 4ST1

The lateral surface area, total surface area and volume of a right hexagonal prism are $180\text{}c{m}^2,180+108\sqrt{3}\text{}c{m}^{2}and270\sqrt{3}c{m}^{3.}$

Explanation of Solution

Given information:

Base-edge of right-hexagonal prism, $b=6\text{ cm}$

Height of right-hexagonal prism, $h=5\text{ cm}$

Calculation:

Calculate lateral surface area of a right-hexagonal prism.

  $\begin{array}{l}\text{Lateral Surface Area}=6bh\\ =6\times 6\times 5\\ =180c{m}^2\end{array}$

And

Calculate total surface area of a right-hexagonal prism.

  $\begin{array}{l}\text{Total Surface Area}=6bh+2(B)\\ =180+2\left(\frac{3\sqrt{3}}{2}{b}^2\right)\\ =180+3\sqrt{3}\left(6^2\right)\\ =180+108\sqrt{3}c{m}^2\end{array}$

And

Calculate volume of a right-hexagonal prism.

  $\begin{array}{l}Volume=Bh\\ =\left(\frac{3\sqrt{3}}{2}{b}^2\right)h\\ =\left(\frac{3\sqrt{3}}{2}\times 6^2\right)\times 5\\ =54\sqrt{3}\times 5\\ =270\sqrt{3}c{m}^3\end{array}$

Therefore, the lateral surface area, total surface area and volume of a right hexagonal prism are $180\text{}c{m}^2,180+108\sqrt{3}\text{}c{m}^{2}and270\sqrt{3}c{m}^{3.}$