Question

1. 11 cm 8 cm volume = ________

Explanation:

Step1: Find the area of the base

The base is a regular hexagon. The formula for the area of a regular hexagon with side - length $s$ is $A = \frac{3\sqrt{3}}{2}s^{2}$. Here, $s = 8$ cm. So, $A=\frac{3\sqrt{3}}{2}\times8^{2}=\frac{3\sqrt{3}}{2}\times64 = 96\sqrt{3}$ $cm^{2}$.

Step2: Calculate the volume of the prism

The volume formula for a prism is $V=A\times h$, where $A$ is the area of the base and $h$ is the height. Given $h = 11$ cm and $A = 96\sqrt{3}$ $cm^{2}$. Then $V=96\sqrt{3}\times11=1056\sqrt{3}\approx1829.2$ $cm^{3}$.

Answer:

$1056\sqrt{3}\text{ cm}^3\approx1829.2\text{ cm}^3$