# Help Been Stuck on these for hours!

1. Calculate the volume of a 5.00 carat diamond.
2. Calculate the force applied to the top of a diver's head (A=300cm^2) by the ocean (rho=1025kg/m^3), if the diver is a) 3.00m below the surface b) 15.0m below the surface

3. Normal atmospheric pressure at sea level is generally considered to be equal to the pressure exerted by a column of mercury 760mm high. Calculate the corresponding pressure in inches of mercury and in Pascals.

4. The hydraulic lift in a service station is capable of raising cars with a mass up to 2000kg. If this is accomplished with a 20.0cm diameter lifting piston, calculate the diameter of the driving piston if the lifting is to be accomplished with a force not to exceed 100N.

5. A raft has a surface area of 100m^2 and a height of 10.0cm. If it is constructed of yellow pine and floating in a lake, calculate how much of the raft will be above the waterline. Also calculate how many people with an average mass of 70.0kg can be placed on the raft to completely submerge it without sinking it.

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1. Calculate the volume of a 5.00 carat diamond.
How much grams is that?
What is the density of diamond?
So....

As you indicate that you've been working on this for hours, I assume that you can show where you got stuck with this and the other problems...

1 carat is equivalent to 0.2 grams

As for the volume, you need to know the density of a diamond. You can analyze the crystal structure (diamonds have their own structure called the diamond cubic). This is a bit complex, so the density is usually given.

two is a plug and chug depth problem

three is a unit conversion problem

four can be a little tough. Use 100N applied to a small piston (taking area into account) and figure out how big the larger piston needs to be in order to apply 19620N (do you see a ratio?)

five you need the density of yellow pine. from ther you can calculate the bouyant force versus the force of the weight of the raft. When you stack people on the raft, ust the same volume as the first part.