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 first need to find the volume of the hexagonal prism and the volume of the triangular prism.
First, let's find the volume of the hexagonal prism:
Base area of the hexagon = (1/2) * (30 cm) * (8 cm) * tan(30°)
Base area of the hexagon = (1/2) * 30 * 8 * tan(30°)
Base area of the hexagon ≈ 93.5307 cm²
Volume of the hexagonal prism = Base area * Height
Volume of the hexagonal prism = 93.5307 cm² * 8 cm = 748.2456 cm³
Next, let's find the volume of the triangular prism:
Base area of the triangle = (1/2) * (15 cm) * (8 cm)
Base area of the triangle = (1/2) * 15 * 8 = 60 cm²
Volume of the triangular prism = Base area * Height
Volume of the triangular prism = 60 cm² * 8 cm = 480 cm³
Total volume of the box = Volume of hexagonal prism + Volume of triangular prism
Total volume of the box = 748.2456 cm³ + 480 cm³ = 1228.2456 cm³
Therefore, the volume of the box is approximately 1228.2456 cm³.