Volume of Composite 3D Figures Practice
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Question
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)
To find the volume of the box, we first need to find the volume of the hexagonal prism and then subtract the volume of the triangular prism at one end.
Volume of hexagonal prism = base area of the hexagon x height
Base area of the hexagon = (perimeter of hexagon x apothem) / 2
Perimeter of hexagon = 6 x side length
Perimeter of hexagon = 6 x 30 = 180 cm
Apothem of hexagon = side length / (2 x tan(π/6))
Apothem of hexagon = 30 / (2 x tan(π/6)) ≈ 15.39 cm
Base area of hexagon = (180 x 15.39) / 2 ≈ 1385.1 cm^2
Volume of hexagonal prism = 1385.1 cm^2 x 8 cm = 11080.8 cm^3
Volume of triangular prism = base area of the base triangle x height
Base area of the base triangle = (15 x 8) / 2 = 60 cm^2
Volume of triangular prism = 60 cm^2 x 8 cm = 480 cm^3
Volume of box = Volume of hexagonal prism - Volume of triangular prism
Volume of box = 11080.8 cm^3 - 480 cm^3 = 10600.8 cm^3
Therefore, the volume of the box is 10600.8 cubic centimeters.