This problem is a tad complex, but the answer should be a relatively simple equation.
A cube has a diagonal of n inches. You are wrapping the cube with a roll of paper which is 12 in x 20 in. Assuming that when you wrap the cube you do not overlap at all, write a function which gives the amount of wrapping paper left over after wrapping this cube with a diagonal of n inches. I know that the problem involves the Pythagorean Theorum (n, diagonal = square root of (length^2 + width^2 + heigh^2) somehow.
So I need to figure out how much wrapping paper is left over after wrapping it around the cube (without overlapping). I've been thinking real hard about this problem all day and I'm hoping some of the fine folks here can provide me with some insight. Thanks in advance!
A cube has a diagonal of n inches. You are wrapping the cube with a roll of paper which is 12 in x 20 in. Assuming that when you wrap the cube you do not overlap at all, write a function which gives the amount of wrapping paper left over after wrapping this cube with a diagonal of n inches. I know that the problem involves the Pythagorean Theorum (n, diagonal = square root of (length^2 + width^2 + heigh^2) somehow.
So I need to figure out how much wrapping paper is left over after wrapping it around the cube (without overlapping). I've been thinking real hard about this problem all day and I'm hoping some of the fine folks here can provide me with some insight. Thanks in advance!
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You need to find the surface area of the cube.
Remember a cube has all sides equal, so if you have a diagonal you can use the pythagorean theorem to calculate the length of each edge. Since edges a and b in the pythagorean theorem are equal, I will represent them with e.
The area of a side can be represented by e^2 and the pythagorean theorem states:
n^2 = 2(e^2)
only solve for e^2 since that is the area of a side.
(n^2)/2 = e^2
Now we have six sides with an area of (n^2)/2, and wrapping paper of 12x20 in or 140 in^2 so we get our function by subtracting the area of the cube from 120:
f(n)=120-6(n^2)/2
Remember a cube has all sides equal, so if you have a diagonal you can use the pythagorean theorem to calculate the length of each edge. Since edges a and b in the pythagorean theorem are equal, I will represent them with e.
The area of a side can be represented by e^2 and the pythagorean theorem states:
n^2 = 2(e^2)
only solve for e^2 since that is the area of a side.
(n^2)/2 = e^2
Now we have six sides with an area of (n^2)/2, and wrapping paper of 12x20 in or 140 in^2 so we get our function by subtracting the area of the cube from 120:
f(n)=120-6(n^2)/2