Question
Calculate a right hexagonal prism with a height of 4 units and a base of 30 units. The volume
Answers
GPT 3.5
To calculate the volume of a right hexagonal prism, we first need to calculate the area of the base.
The formula for the area of a regular hexagon is:
Area = (3√3/2) * s^2,
where s is the length of a side of the hexagon.
Since the base of the hexagonal prism is a regular hexagon, and the side length of the hexagon is equal to the height of the prism, which is 4 units, we can calculate the area of the base as follows:
Area = (3√3/2) * 4^2
Area = (3√3/2) * 16
Area = 24√3 square units
Now that we have the area of the base, we can calculate the volume of the hexagonal prism by multiplying the area of the base by the height of the prism:
Volume = Area of base * height
Volume = 24√3 * 4
Volume = 96√3 cubic units
Therefore, the volume of the right hexagonal prism is 96√3 cubic units.
The formula for the area of a regular hexagon is:
Area = (3√3/2) * s^2,
where s is the length of a side of the hexagon.
Since the base of the hexagonal prism is a regular hexagon, and the side length of the hexagon is equal to the height of the prism, which is 4 units, we can calculate the area of the base as follows:
Area = (3√3/2) * 4^2
Area = (3√3/2) * 16
Area = 24√3 square units
Now that we have the area of the base, we can calculate the volume of the hexagonal prism by multiplying the area of the base by the height of the prism:
Volume = Area of base * height
Volume = 24√3 * 4
Volume = 96√3 cubic units
Therefore, the volume of the right hexagonal prism is 96√3 cubic units.