If the surface area of a certain cube is 2400, what is...

[BTGmoderatorLU]

If the surface area of a certain cube is 2400, what is its volume?

A. 8000(√6)^3
B. 1000(√6)^3
C. 8000
D. 6400
E. 4000

The OA is C.

We know that the surface area of a cube is 6s^2, then
$$6s^2=2400\ \Rightarrow s^2=400\ \Rightarrow s=20$$
Also, we know that the volume of a cube is s^3, then
$$s^3=20^3=8000$$
Experts, any suggestion about this PS question? Thanks in advance.

[EconomistGMATTutor]

If the surface area of a certain cube is 2400, what is its volume?

A. 8000(√6)^3
B. 1000(√6)^3
C. 8000
D. 6400
E. 4000

The OA is C.

We know that the surface area of a cube is 6s^2, then
$$6s^2=2400\ \Rightarrow s^2=400\ \Rightarrow s=20$$
Also, we know that the volume of a cube is s^3, then
$$s^3=20^3=8000$$
Experts, any suggestion about this PS question? Thanks in advance.

Hi LUANDATO.

Your answer is good. This is the correct way to solve this PS question.

Since a cube is formed by 6 faces that are squares, then 6L^2=2400 and therefore L=20.

And the volume of a cube is L^3, hence the volume is (20)^3=8000. Therefore, the correct answer is the option C.

I hope this answer also can help you.

Regards.

[Scott@TargetTestPrep]

If the surface area of a certain cube is 2400, what is its volume?

A. 8000(√6)^3
B. 1000(√6)^3
C. 8000
D. 6400
E. 4000

Suppose we have a cube such that the length of each edge is x. Since there are 6 faces on the cube, and each face has an area of x^2, then the surface area is the sum of the 6 faces' areas. Thus, we have:

6x^2 = 2400

x^2 = 400

x = 20

Thus the volume of the cube is 20^3 = 8000.

Answer: C