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
Geometry question
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 DanaJ
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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 cubeshaped object  I used a staples box).
So the answer is indeed C
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 cubeshaped object  I used a staples box).
So the answer is indeed C
agreedDanaJ 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 cubeshaped object  I used a staples box).
So the answer is indeed C
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The question says that the volume is x cubic feet and the area is x square feet.billbo29 wrote:how can you set a^3 equal to 6a^2
Given an edge length, a, the volume of a cube = aÂ³ cubic feet.
Given an edge length, a, the total area of the cube = 6(aÂ²) square feet.
x = aÂ³ = 6(aÂ²)
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The stem says that Volume = Surface Area. Since volume = aÂ³ and surface area = 6aÂ², we then can set those equal, and work from there.billbo29 wrote:how can you set a^3 equal to 6a^2