GRE Math : Cubes
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Example Questions
Example Question #2 : How To Find The Volume Of A Cube
What is the volume of a cube with surface area of 
Recall that the equation for the surface area of a cube is merely derived from the fact that the cube's faces are made up of 
For our values, this is:
Solving for 
Now, the volume of a cube is merely:
Therefore, for 
Example Question #3 : How To Find The Volume Of A Cube
A cube has a volume of 64, what would it be if you doubled its side lengths?
To find the volume of a cube, you multiple your side length 3 times (s*s*s).
To find the side length from the volume, you find the cube root which gives you 4
Doubling the side gives you 8
The volume of the new cube would then be 512
Example Question #1 : How To Find The Surface Area Of A Cube
A rectangular box is 6 feet wide, 3 feet long, and 2 feet high. What is the surface area of this box?
72 sq ft
36 sq ft
64 sq ft
48 sq ft
22 sq ft
72 sq ft
The surface area formula we need to solve this is 2ab + 2bc + 2ac. So if we let a = 6, b = 3, and c = 2, then surface area:
= 2(6)(3) + 2(3)(2) +2(6)(2)
= 72 sq ft.
Example Question #2 : How To Find The Surface Area Of A Cube
What is the surface area of a rectangular box that is 3 feet high, 6 feet long, and 4 feet wide?
108
72
84
144
96
108
Surface area of a rectangular solid
= 2lw + 2lh + 2wh
= 2(6)(4) + 2(6)(3) + 2(4)(3)
= 108
Example Question #3 : How To Find The Surface Area Of A Cube
A large cube is made by fitting 8 smaller, identical cubes together. If the volume of each of the smaller cubes is 27, what is the surface area of the large cube?
Since the volume of the smaller cubes with edges, 
The large cube has edges 
So the surface area of the large cube is:
Example Question #2 : How To Find The Surface Area Of A Cube
Quantity A:
The surface area of a cube with a volume of 
Quantity B:
The volume of a cube with a surface area of 
Quantity B is greater.
The relationshp cannot be determined from the information given.
Both quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship can be determined, because it is possible to find the surface area of a cube from the volume and vice versa.
Quantity A:
To find the surface area of the cube, you must find the side length. To find the side length from the volume, you must find the cube root.
Find the cube root of the volume.
Insert into surface area equation.
Quantity B:
To find the volume of a cube, you must find the side length. To find the side length from the surface area, you must divide by 6, then find the square root of the result. Then, cube that result.
Divide by 6.
Square root.
Now, to find the volume.
Quantity B is greater.
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