SOLUTION: You have a cube of gold. Your friend (even though she may not be your friend much longer) has a cube of gold that is twice as long (and wide and high). Your friend's cube weights [
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-> SOLUTION: You have a cube of gold. Your friend (even though she may not be your friend much longer) has a cube of gold that is twice as long (and wide and high). Your friend's cube weights [
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Question 182723: You have a cube of gold. Your friend (even though she may not be your friend much longer) has a cube of gold that is twice as long (and wide and high). Your friend's cube weights [ ] as much as yours, and it has [ ] times the surface area. You also have a spherical diamond. Your friend has a spherical diamond of twice the diameter of yours. Your friend's cube weights [ ] as much as yours, and it has [ ] the surface area. Answer by solver91311(24713) (Show Source):
The the weights of two solid masses of similar material are proportional to their volumes.
The volume of your cube, of edge length s is given by:
Since the side length of the larger cube is 2s, the volume of the larger cube must be:
So your friend's cube has 8 times the volume and therefore weighs 8 times as much as yours.
The surface area of a cube of edge length s is found by considering that a cube has 6 faces, each of which has an area , therefore the total surface area of your cube is:
And the total surface area of your friend's cube is:
And your friend's cube has 4 times the surface area as yours.
The problem with the sphere is done in the same fashion. The formulas for volume and surface area for a sphere are:
Hint: If your friend's sphere has twice the diameter, it also has twice the radius.
