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 [

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): You can put this solution on YOUR website!

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.

John

RELATED QUESTIONS
You have a cube of gold. Your friend (even though she may not be your friend much longer) (answered by Alan3354)

Your friend has a cube of gold. You have a cube of gold that weighs twice as much. Your... (answered by Alan3354)

Gold has a density of 19 320kg/m3. A salesman wants to sell you a metallic cube that... (answered by ikleyn)

Gold has a density of 19.4 g/Cm3. A cube of gold measures 4.23 cm on each edge. What is... (answered by solver91311)

Marina has a gold bracelet that weighs 90 grams. 45% of the bracelet is pure gold. How... (answered by ikdeep)

A goldsmith has 60 pounds of an alloy that is 50% pure gold. How many pounds of an alloy... (answered by Fombitz)

i have this question that i have no idea what to do: you have just on a game show on... (answered by ankor@dixie-net.com)

A friend who hears that you are taking a statistics course asks for help with a specific... (answered by stanbon)