Chapter 12, Problem 14RP

To determine

To Calculate: The surface area and volume of the box

Answer to Problem 14RP

The surface area and volume of the box are $216\sqrt{3}$ cm ${}^2$ and $4320\sqrt{3}$ cm ${}^3$

Explanation of Solution

Given information:

The side of hexagon = $12$ cm

The height of the box = $20$ cm

Formula used:

Surface area of hexagon = $\frac{3\sqrt{3}{s}^2}{2}$

(Where, “ s ” is side)

Volume of hexagon = area of hexagon $\times$ height

Calculation:

Here, surface area of hexagon = $\frac{3\sqrt{3}{s}^2}{2}$

(Where, “ s ” is side)

  → $3\sqrt{3}\times \frac{144}{2}$

  → $216\sqrt{3}$

Now, volume of hexagon = area of hexagon $\times$ height

  → $216\sqrt{3}\times 20$

  → $4320\sqrt{3}$

Conclusion: Hence, the surface area and volume of the box are $216\sqrt{3}$ cm ${}^2$ and $4320\sqrt{3}$ cm ${}^3$