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
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page 11 of 12
To find the volume of the box, we need to calculate the volume of both the hexagonal prism and the triangular prism separately and then add them together.
For the hexagonal prism:
Area of the hexagon = (3√3)/2 * base * height
Area of the hexagon = (3√3)/2 * 30 * 30
Area of the hexagon = (3√3)/2 * 900
Area of the hexagon = 1309.7 cm^2
Volume of the hexagonal prism = base area * height
Volume of the hexagonal prism = 1309.7 * 8
Volume of the hexagonal prism = 10477.6 cm^3
For the triangular prism:
Volume of the triangular prism = (1/2) * base * height * width
Volume of the triangular prism = (1/2) * 15 * 8 * 30
Volume of the triangular prism = 1800 cm^3
Total volume of the box = Volume of hexagonal prism + Volume of triangular prism
Total volume of the box = 10477.6 + 1800
Total volume of the box = 12277.6 cm^3
Therefore, the volume of the box is 12277.6 cm^3.