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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To find the volume of the box, we need to find the volume of both the hexagonal prism and the triangular prism, and then add them together.
Volume of hexagonal prism:
Base area = (1/2) * perimeter of hexagon * apothem
Base area = (1/2) * (6 * 30) cm * (15 cm/2)
Base area = 450 cm^2
Volume = base area * height
Volume = 450 cm^2 * 8 cm
Volume = 3600 cm^3
Volume of triangular prism:
Base area = (1/2) * base * height
Base area = (1/2) * 15 cm * 8 cm
Base area = 60 cm^2
Volume = base area * height
Volume = 60 cm^2 * 8 cm
Volume = 480 cm^3
Total volume = Volume of hexagonal prism + Volume of triangular prism
Total volume = 3600 cm^3 + 480 cm^3
Total volume = 4080 cm^3
Therefore, the volume of the box is 4080 cm^3.
wrong
Apologies for the error in the previous calculation. Let's re-calculate the volume of the box.
Volume of the hexagonal prism:
Base area = 3 * (sqrt(3)/2) * (15 cm)^2 ≈ 584.6 cm²
Volume = Base area * height = 584.6 cm² * 8 cm = 4676.8 cm³
Volume of the triangular prism:
Base area = (1/2) * base * height = (1/2) * 15 cm * 8 cm = 60 cm²
Volume = Base area * height = 60 cm² * 8 cm = 480 cm³
Total volume = Volume of hexagonal prism + Volume of triangular prism = 4676.8 cm³ + 480 cm³ = 5156.8 cm³
Therefore, the correct volume of the box is 5156.8 cm³.