A solid aluminum sphere has a radius of 1.84 m and a temperature of 77.5 °C. The sphere is then completely immersed in a pool of water whose temperature is 26.7 °C. The sphere cools, while the water temperature remains nearly at 26.7 °C, because the pool is very large. The sphere is weighed in the water immediately after being submerged (before it begins to cool) and then again after cooling to 26.7 °C. Use Archimedes' principle to find the magnitude of the difference between the weights.
Volume of the sphere: (4/3) pi (R)^3
and change in volume: coefficient of volume expansion for aluminum (69 x 10^-6) * (Initial Volume: 26.094) * (Change in Temp: -50.8)
= - .0915
This is the other equation I have:
difference in weight = -(density)(gravity)(volume)
But the answer I get isn't right...
The Attempt at a Solution
I think everything I am doing is right up until the part about finding the difference in weights. I don't know what equation to use, or how to use it I guess. Any help would be appreciated.