Problem Solving

If the volume of a cube is x cubic feet and the total surface area of the cube is x square feet,then what is the total length, in feet, of all the cube’s edges?

(A) 24 (B) 60(C) 72(D) 120(E) 144

OA C. 72

Thanks

Say a = length of cube's side. Then you get that:
volume = a^3
surface area = 6a^2 (since there are 6 sides, each a^2 in surface).
This means that a^3 = 6a^2, with a = 6 the only positive solution.
Now, the total length you are looking for is 12 * 6 = 72 feet, since there are 12 edges (you can verify this by using any cube-shaped object - I used a staples box).

So the answer is indeed C

DanaJ wrote:Say a = length of cube's side. Then you get that:
volume = a^3
surface area = 6a^2 (since there are 6 sides, each a^2 in surface).
This means that a^3 = 6a^2, with a = 6 the only positive solution.
Now, the total length you are looking for is 12 * 6 = 72 feet, since there are 12 edges (you can verify this by using any cube-shaped object - I used a staples box).

So the answer is indeed C

agreed

Dana,

Excuse my ignorance, but where did you get the 12 in 12 * 6 from?

Thanks

ellexay wrote:Dana,

Excuse my ignorance, but where did you get the 12 in 12 * 6 from?

Thanks

there are 12 edges for the cube.. if you want you draw picture and count id..

how can you set a^3 equal to 6a^2

billbo29 wrote:how can you set a^3 equal to 6a^2

The question says that the volume is x cubic feet and the area is x square feet.

Given an edge length, a, the volume of a cube = a³ cubic feet.

Given an edge length, a, the total area of the cube = 6(a²) square feet.

x = a³ = 6(a²)

billbo29 wrote:how can you set a^3 equal to 6a^2

The stem says that Volume = Surface Area. Since volume = a³ and surface area = 6a², we then can set those equal, and work from there.