Question

c. a hexagonal prism that has a height of 5 inches and a base with dimensions of 3 inches per side and length from one flat side to the other of 10 inches we know

Explanation:

Step1: Find area of hexagonal base

The area formula for a regular hexagon with side - length $s$ and apothem $a$ is $A = \frac{1}{2}\times perimeter\times apothem$. The perimeter of the hexagon $P=6s$, where $s = 3$ inches, so $P = 6\times3=18$ inches. The apothem $a = 5$ inches (since the distance from one flat side to the other is 10 inches, the apothem is half of that). Then $A_{base}=\frac{1}{2}\times18\times5 = 45$ square inches.

Step2: Calculate volume of prism

The volume formula for a prism is $V=A_{base}\times h$, where $h$ is the height of the prism. Given $h = 5$ inches and $A_{base}=45$ square inches. So $V=45\times5=225$ cubic inches.

Answer:

225 cubic inches