The volume of cube I is 331 m^3 less than the volume of cube II. If an edge of cube I is 10 meters, an edge of cube II is
A. 14 meters
B. 13 meters
C. 12 meters
D. 11 meters
V1 = 1000
V2 = 1331
V1/V2 = (10/L)^3, where L = side of larger cube
1000/1331 = 1000/L^3
L^3 = 1331
L = Cuberoot(1331)
11 meters
To solve this problem, you need to understand that the volume of a cube is determined by the formula V = a^3, where "V" is the volume and "a" is the length of one edge of the cube.
Let's assume that the edge length of cube II is "x" meters. According to the information given, the volume of cube I is 331 m^3 less than the volume of cube II. Therefore, we can write the equation:
(x^3) - (10^3) = 331
Simplifying this equation, we have:
x^3 - 1000 = 331
Next, we can move 1000 to the other side of the equation:
x^3 = 331 + 1000
x^3 = 1331
Finally, we can find the value of "x" by taking the cube root of both sides:
x = cube root of 1331
By calculating the cube root of 1331, we find that x is equal to 11 meters.
Therefore, the correct answer is D. 11 meters, which represents the length of one edge of cube II.
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