ACT Math · Area and volume

A rectangular prism has length 5, width 4, and height 3. What is its total surface area?

A rectangular prism has length 5, width 4, and height 3. What is its total surface area?

Answer and explanation

Answer: H: 94

A rectangular prism has three pairs of identical faces. The surface area is 2(lw+lh+wh)=2(5⋅4+5⋅3+4⋅3)=2(20+15+12)=2(47)=942(lw+lh+wh)=2(5\cdot4+5\cdot3+4\cdot3)=2(20+15+12)=2(47)=94, choice H. Choice F (4747) is half the surface area, because it counts each pair of faces once instead of twice. Choice G (6060) is the volume 5⋅4⋅35\cdot4\cdot3, a different quantity measured in cubic units. Choice J (120120) is double the volume. Make sure the question asks for total surface area, which includes all six faces, rather than volume.

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