To calculate the volume of the hexagonal prism box, we first need to find the area of the base (hexagon) and then multiply it by the height of the prism.
The area of a regular hexagon can be calculated using the formula:
Area = (3√3/2) x side length squared
In this case, the side length of the hexagon is equal to the distance between the two longer parallel sides of the prism, which is 30 cm.
Area = (3 x √3/2) x 30^2
Area = (3 x 1.732/2) x 900
Area = 2.598 x 900
Area = 2338.2 cm^2
Now, we can find the volume of the hexagonal prism box:
Volume = Area of base x height
Volume = 2338.2 cm^2 x 8 cm
Volume = 18705.6 cm^3
Therefore, the volume of the box is 18705.6 cm^3.
Use the image to answer the question.
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?
box cm3
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