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.

a^2=9X^2

Lets take the sqrt of both sides

a=3X

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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