To find the volume of the hexagonal prism, we first need to find the area of the hexagonal base.
The formula for the area of a regular hexagon is:
Area = (3√3 x side length^2) / 2
In this case, the side length of the hexagon is 30 cm.
Area = (3√3 x 30^2) / 2
Area = (3√3 x 900) / 2
Area = 1350√3 / 2
Area = 675√3 cm^2
Now, to find the volume of the hexagonal prism, we multiply the base area by the height:
Volume = 675√3 x 8
Volume = 5400√3 cm^3
Therefore, the volume of the box is 5400√3 cm^3.
An illustration shows a hexagonal prism with the label Choosy Cheesy on the top surface. The height of the hexagonal prism is 8 centimeters. The two longer parallel sides of the hexagonal prism each measure 30 centimeters in length. One end of the prism is marked with a dashed line measuring 15 centimeters across, joining the two opposite vertices of the parallel edges, forming a triangular prism with a perpendicular measure of 8 centimeters.
A sample of gourmet cheeses came in this box. What is the volume of the box?
Your answer: cm^3
1 answer