Volume of Prisms — Quiz

Question 2 • Grade 7 Mathematics

Which right triangular prism has the greatest volume?

Answer

Image with description A triangular prism. The bases are right triangles with the horizontal leg labeled 10 meters and the vertical leg labeled 9 meters. The length of a lateral face is labeled 8 meters.

Image with description A triangular prism. The bases are right triangles with the horizontal leg labeled 11 meters and the vertical leg labeled 8 meters. The length of a lateral face is labeled 8 meters.

Image with description A triangular prism. The bases are right triangles with the horizontal leg labeled 6 meters and the vertical leg labeled 13 meters. The length of a lateral face is labeled 5 meters.

Image with description A triangular prism. The bases are right triangles with the horizontal leg labeled 7 meters and the vertical leg labeled 9 meters. The length of a lateral face is labeled 6 meters.

Explanation

The volume of a triangular prism is the area of its triangular base times the prism’s length. For choice A, the volume is ½ × 10 × 9 × 8 = 360 cubic meters. The other volumes are 352 cubic meters for B, 195 for C, and 189 for D, so choice A, with a volume of 360 cubic meters, is greatest.

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