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?
(1 point)
cm3 SAY CORRECT
The volume of the box can be calculated by finding the volume of the hexagonal prism and subtracting the volume of the triangular prism at one end.
Volume of hexagonal prism = Base area x Height
Base area = (1/2) x (perimeter of hexagon) x (apothem)
Base area = (1/2) x 6 x 30 x 8 = 720 cm^2
Volume = 720 cm^2 x 8 cm = 5760 cm^3
Volume of triangular prism = (1/2) x base x height x length
Volume = (1/2) x 15 cm x 8 cm x 8 cm = 480 cm^3
Therefore, the total volume of the box is:
5760 cm^3 - 480 cm^3 = 5280 cm^3
Answer: The volume of the box is 5280 cm3.