Regular hexagonal prism

Text

A right prism has a regular hexagon of side $6$ cm as base and height $10$ cm. Find the total surface area and the volume. (Take $\sqrt3\approx1.732$.)

Solution

Area of the regular hexagon: $\mathcal A_b=\dfrac{3\sqrt3}{2}\ell^2=\dfrac{3\sqrt3}{2}\cdot36=54\sqrt3\approx93.53$ cm$^2$; perimeter $36$ cm. Lateral surface: $36\cdot10=360$ cm$^2$. Total surface: $S_t=360+2\cdot54\sqrt3=360+108\sqrt3\approx547.06$ cm$^2$. Volume: $V=54\sqrt3\cdot10=540\sqrt3\approx935.31$ cm$^3$. $\boxed{S_t=360+108\sqrt3\approx547.06\ \text{cm}^2;\ V=540\sqrt3\approx935.31\ \text{cm}^3}$