ACT Math · Area and volume

A storage container is shaped like a rectangular prism measuring 6 by 4 by 5, topped with a pyramid of the same base and a height of 3.…

A storage container is shaped like a rectangular prism measuring 6 by 4 by 5, topped with a pyramid of the same base and a height of 3. What is the total volume of the container?

Answer and explanation

Answer: J: 144

The container is a prism with a pyramid on top. The prism has volume 6⋅4⋅5=1206\cdot4\cdot5=120. The pyramid has the same base, 6⋅4=246\cdot4=24, and height 33, so its volume is 13(24)(3)=24\frac{1}{3}(24)(3)=24. The total is 120+24=144120+24=144, choice J. Choice F (120120) leaves out the pyramid. Choice G (192192) uses 24⋅3=7224\cdot3=72 for the pyramid, forgetting the factor 13\frac{1}{3}. Choice H (168168) uses 23\frac{2}{3} for the pyramid. A pyramid holds exactly one third of the prism with the same base and height.

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