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?
cm3
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.