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Area and volume SAT question
Math · Geometry and Trigonometry · Hard · Answer it here, explanation included.
A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?
ExplanationShow
Choice B is correct. The surface area of a cube with side length s is equal to 
. Since the surface area is given as 54 square meters, the equation 
can be used to solve for s. Dividing both sides of the equation by 6 yields 
. Taking the square root of both sides of this equation yields 
and 
. Since the side length of a cube must be a positive value, 
can be discarded as a possible solution, leaving 
. The volume of a cube with side length s is equal to 
. Therefore, the volume of this cube, in cubic meters, is 
, or 27.
Choices A, C, and D are incorrect and may result from calculation errors.
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