Which expression correctly gives the volume of a rectangular prism?

Which expression correctly gives the volume of a rectangular prism?

• A. l w h
• B. 2(lw+lh+wh)
• C. (1/3) B h
• D. B h^2

Answer: (A)

Volume measures how much space is inside a three-dimensional shape. For a rectangular prism, you can think of filling it with unit cubes along its length, width, and height. Each layer across the height has l × w unit squares, and there are h such layers, so the total number of unit cubes—and thus the volume—is l × w × h. That’s why the expression l w h is the one that correctly gives the volume, in cubic units. The other expressions describe different quantities: 2(lw + lh + wh) is the surface area, not volume; (1/3)Bh is the volume formula for a pyramid with base area B and height h; and Bh^2 doesn’t correspond to the standard volume formula for a rectangular prism.

Volume measures how much space is inside a three-dimensional shape. For a rectangular prism, you can think of filling it with unit cubes along its length, width, and height. Each layer across the height has l × w unit squares, and there are h such layers, so the total number of unit cubes—and thus the volume—is l × w × h. That’s why the expression l w h is the one that correctly gives the volume, in cubic units.

The other expressions describe different quantities: 2(lw + lh + wh) is the surface area, not volume; (1/3)Bh is the volume formula for a pyramid with base area B and height h; and Bh^2 doesn’t correspond to the standard volume formula for a rectangular prism.