Question

the edge length, in millimeters (mm), of cube y is 233 times the edge length, in mm, of cube x. the surface area, in mm², of cube y is n times the surface area, in mm², of cube x. what is the value of n?
a 233
b 1,398
c 54,289
d 325,734

Explanation:

Step1: Recall the surface area formula for a cube

The surface area formula of a cube is \(S = 6s^{2}\), where \(s\) is the edge - length of the cube.
Let the edge - length of cube \(X\) be \(s_{X}\), then the edge - length of cube \(Y\) is \(s_{Y}=233s_{X}\).

Step2: Calculate the surface areas of cube \(X\) and cube \(Y\)

The surface area of cube \(X\) is \(S_{X}=6s_{X}^{2}\).
The surface area of cube \(Y\) is \(S_{Y}=6s_{Y}^{2}\). Substitute \(s_{Y} = 233s_{X}\) into the formula:

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Since \(S_{X}=6s_{X}^{2}\), and \(n=\frac{S_{Y}}{S_{X}}\), then \(n = 233^{2}\).

Step3: Calculate \(233^{2}\)

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Answer:

C. \(54,289\)