1. Calculate the volume of a 5.00 carat diamond.(10)
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(20)
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 and in Pascals.(20)
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.(20)
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.(30)
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.