Your friend has a cube of gold. You have a cube of gold that weighs twice as much. Your cube is 1.26as long as your friends, and it has 1.587 times the surface area. You can imagine how this would work with a spherical diamond, so we won't repeat that part here. Here is another question: The ratio of the weight of your cube and the surface area of your cube is ___ times as large as the corresponding ratio of your friend's cube.
no
To find the answer, let's break down the given information and solve for the ratio.
Let's assume the weight of your friend's cube is W (in some unit), and the weight of your cube is twice that, so it would be 2W.
We are given that your cube is 1.26 times longer than your friend's cube. So, if your friend's cube has a side length of S (in some unit), then your cube's side length would be 1.26S.
Now, let's calculate the surface area ratio. The surface area of your friend's cube is given by 6S^2 (the surface area of a cube is 6 times the side length squared). The surface area of your cube would be 1.587 times that. Therefore, the surface area of your cube is 1.587 * 6S^2 = 9.522S^2.
The weight-to-surface area ratio for your friend's cube is W/6S^2.
Similarly, the weight-to-surface area ratio for your cube is 2W/9.522S^2.
To find the ratio of the weight-to-surface area ratios, we divide one by the other:
(2W/9.522S^2) / (W/6S^2)
Simplifying this expression gives:
(2W/9.522S^2) * (6S^2/W)
The S^2 terms and the W terms cancel out, and we are left with:
2/9.522 * 6 = 0.126 * 6 = 0.756
Therefore, the ratio of the weight of your cube to the surface area of your cube is 0.756 times as large as the corresponding ratio for your friend's cube.