SAT Question of the Day July 27th 2013

What is the volume of a cube with surface area 54 times (x ^ 2)?

A.     9 times (x ^ 2)

B.     27 times (x^3)

C.     81 times (x ^ 2)

D.     81 times (x ^ 3)

E.     729 times (x ^ 3)

We have a geometry problem. Remember you have a formula sheet on the first page – if you don’t remember the formulas you can always go there and check.

A cube with a side of a has a volume equal to a^3 (aXaXa)

All we need to do is to find what is the value of a in terms of X.

We are given the surface area of the cube. This is the sum of the area of the six faces of cube – each is a^2 units.

Surface area is then 6Xa^2.

If we take 54X^2 and divide it to 6 we will obtain the value of one face.


Lets take the sqrt of both sides


Now we know the value (in terms of X) of the side of the cube. The volume is a^3:

3X times 3X times 3X or (3X)^3 = 27X^3

46% out of 190,000 got it right.

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