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?
(1 point)
cm3
The volume of the hexagonal prism can be calculated using the formula V = Bh, where B is the area of the base and h is the height. In this case, the base is a hexagon, which can be divided into six equilateral triangles. The area of one of these triangles can be found using the formula A = (1/2)bh, where b is the base and h is the height.
Since the base of each triangle is 15 cm and the height is 8 cm, the area of one triangle is (1/2)(15)(8) = 60 cm^2.
Since there are six of these triangles in the hexagon base, the total base area is 6*60 = 360 cm^2.
Therefore, the volume of the hexagonal prism is V = 360 * 8 = 2880 cm^3.