SAT Math formula sheet · all 24 · Geometry and Trigonometry · #22 of 24

Volume and surface area on the SAT: How It Is Tested

Area and volume

Volume and Surface Area diagram for the SAT: The SAT gives you the rectangular prism on its reference sheet, but it does not give you surface area. You need to be ab
What it is really testingThe SAT gives you the rectangular prism on its reference sheet, but it does not give you surface area. You need to be able to derive surface area by looking at the figure, or memorize it from here. The square prism and the cube are variations of a rectangular prism, with two sides the same and all three sides the same, respectively.

The question from the sheet

Hard
SAT Geometry and Trigonometryanswer 24576
A cube has a volume of 262,144262{,}144 cubic units. What is the surface area, in square units, of this cube?
Student-produced response: 24576

How the diagram applies

  1. Cube: Volume =x3= x^{3}, so x3=262,144x^{3} = 262{,}144 and x=64x = 64 (check: 64⋅64⋅64=262,14464 \cdot 64 \cdot 64 = 262{,}144).
  2. Surface area =6x2=6(64)2=6(4,096)=24,576= 6x^{2} = 6(64)^{2} = 6(4{,}096) = 24{,}576.

Answer: 24576

That is 1 of 24.

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Common Questions

It comes up as an SAT area and volume question. The SAT gives you the rectangular prism on its reference sheet, but it does not give you surface area. You need to be able to derive surface area by looking at the figure, or memorize it from here. The square prism and the cube are variations of a rectangular prism, with two sides the same and all three sides the same, respectively.

Cube: Volume = x^3, so x^3 = 262,144 and x = 64 (check: 64 × 64 × 64 = 262,144). Surface area = 6x^2 = 6(64)^2 = 6(4,096) = 24,576.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Volume and Surface Area is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.