Final answer:
The volume of a regular hexagonal prism with a side length of 10 cm and a height of 4 cm is approximately 1039 cm³ when rounded to the nearest cubic centimeter.
Step-by-step explanation:
To find the volume of a regular hexagonal prism, we first need to calculate the area of the hexagonal base and then multiply by the height of the prism. The formula for the area of a regular hexagon with side length a is given by:
Area of hexagon = \((3\sqrt{3}/2)\) \(a^2\)
For a side length of 10
Area of hexagon = \((3\sqrt{3}/2)\) \((10 cm)^2\) = 259.81 cm² (approximately)
Now, multiply the area of the base by the height of the prism, which is 4 cm:
Volume = Area of base \(\times\) Height = 259.81 cm² \(\times\) 4 cm = 1039.24 cm³
However, rounding to the nearest cubic centimeter, the volume is approximately 1039 cm³.