Chapter 12.4, Problem 12PSB

Solution

To Calculate: The volume and surface area of the regular hexagonal right prism.

The volume of the regular hexagonal right prism = $540\sqrt{3}$ unit ${}^3$ and

The surface area = $108\sqrt{3}+360$ unit ${}^2$

Given information:

The measures of the given lengths are as follows:

Height of hexagonal right prism (h) = $10$

Side of hexagonal right prism (a) = $6$

Formula used:

Here, we are using the formula:

Surface area of hexagonal right prism = $3\sqrt{3}{a}^2+6ah$

(Where, “a” is side and “h” is height)

Volume of hexagonal right prism = $\frac{3\sqrt{3}}{2}\times a^2\times h$

(Where, “a” is side and “h” is height)

Calculation:

Here, Surface area of hexagonal right prism = $3\sqrt{3}{a}^2+6ah$

(Where, “a” is side and “h” is height)

➜ $3\sqrt{3}\times {\left(6\right)}^2+6\times 6\times 10$

➜ $108\sqrt{3}+360$

Now, Volume of hexagonal right prism = $\frac{3\sqrt{3}}{2}\times a^2\times h$

(Where, “a” is side and “h” is height)

➜ $\frac{3\sqrt{3}}{2}\times {\left(6\right)}^2\times 10$

➜ $\frac{3\sqrt{3}\times 36}{2}\times 10$

➜ $540\sqrt{3}$

Conclusion: Hence, the volume of the regular hexagonal right prism = $540\sqrt{3}$ unit ${}^3$ and

The surface area = $108\sqrt{3}+360$ unit ${}^2$