Use the image to answer the question.

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?

cm3

Answer 1

To find the volume of the box, we need to calculate the volume of the hexagonal prism and the volume of the triangular prism separately.

1. Volume of the hexagonal prism:
Height = 8 cm
Base area = (1/2) x 30 cm x 15 cm (the longer sides of the hexagon)
Volume = Base area x Height
Volume = (1/2) x 30 cm x 15 cm x 8 cm
Volume = 1800 cm3

2. Volume of the triangular prism:
Base area = (1/2) x 15 cm x 8 cm (the base of the triangle)
Height = 30 cm (distance between the two parallel edges of the hexagonal prism)
Volume = Base area x Height
Volume = (1/2) x 15 cm x 8 cm x 30 cm
Volume = 1800 cm3

Total volume of the box = Volume of hexagonal prism + Volume of triangular prism
Total volume = 1800 cm3 + 1800 cm3
Total volume = 3600 cm3

Therefore, the volume of the box is 3600 cm3.