1) A homemade wooden raft is 1.45 m wide and 3.05 m long with vertical sides. The bottom of the raft is 0.632 m below the water surface. What is the weight (in newtons) of the raft and its cargo, if it is floating in fresh water?

2) A hot air balloon (excluding the hot air inside) together with its cargo has a mass of 420 kg. The balloon holds 715 m³ of hot air. It is floating at a constant height in air with a density of 1.28 kg/m³. What is the density (in kg/m³) of the hot air in the balloon?

3) A rock is suspended from a force probe which reads 10.7 N. A beaker of water is raised up so that the rock is totally submerged in water. The force probe now reads 7.00 N. How many times greater is the density of the rock than the density of water?

4) A toy crown when weighed in air, has a weight of 8.00 N. When completely immersed in fresh water, however, it has a weight of 4.15 N. Find the volume of the toy crown in cm³.

5) Ernie's rubber ducky is floating in the bathtub with 10.3% of its volume beneath the surface of the water. Find the average density of the rubber ducky (in kg/m³).

6) A solid circular cylinder floats with its axis oriented vertically. It has a radius of 1.76 m, a height of 0.573 m and weighs 37.2 kN. To what depth (in metres) will it sink when it is floating in fresh water?

7) Gilligan is trying to escape a desert island with his friends. They make a raft is made from 9 logs lashed together. Each log is 30.4 cm in diameter and has a length of 5.07 m. How many people can the raft hold before they start getting their feet wet? Assume each person has the average mass of 67.7 kg and that the density of water and wood is 1000 kg/m³and 600 kg/m³, respectively

8) A lost treasure chest is found resting on the ocean floor and completely submerged. The treasure chest is 6.18 m long, 2.02 m wide, and 2.99 m high. Treasure hunters attach a spherical balloon to the top of the treasure chest and inflate it with air pumped down from the surface. When the balloon's radius is 1.41 m, the treasure chest just begins to rise toward the surface. What is the mass (in kg) of the treasure chest? Ignore the mass of the balloon and the air within it. Donot neglect the buoyant force exerted on the treasure chest by the water. The density of seawater is 1025 kg/m³.