Volume of Composite 3D Figures Practice
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Question
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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?
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, and then add them together.
Volume of the hexagonal prism:
First, calculate the area of the base, which is a hexagon.
Area of a regular hexagon = (3√3 x s^2) / 2, where s is the length of a side
Area = (3√3 x 30^2) / 2
Area = (3√3 x 900) / 2
Area = 1551.32 square centimeters
Now, find the volume of the hexagonal prism:
Volume = base area x height
Volume = 1551.32 x 8
Volume = 12410.56 cubic centimeters
Volume of the triangular prism:
Area of the base triangle = (1/2) x base x height
Area = (1/2) x 15 x 8
Area = 60 square centimeters
Now, find the volume of the triangular prism:
Volume = base area x height
Volume = 60 x 8
Volume = 480 cubic centimeters
Now, add the volumes of both prisms together:
Total volume = 12410.56 + 480
Total volume = 12890.56 cubic centimeters
Therefore, the volume of the box is 12890.56 cubic centimeters.