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.
If the surface area of a certain cube is 2400, what is...
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Hi LUANDATO.LUANDATO wrote: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.
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.
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BTGmoderatorLU wrote: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
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