If a sealed balloon filled with air has a volume of 6 cubic inches at 99 feet, what will its volume be at 33 feet?

To determine the volume of the balloon at a shallower depth, it is essential to understand the principles of gas laws, specifically Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature remains constant. As a diver ascends, the water pressure decreases, allowing the volume of any gas-filled container, such as the balloon in this scenario, to expand.

At 99 feet, the pressure is significantly higher due to the weight of the water above, which compresses the air within the balloon. As the diver ascends to 33 feet, the pressure decreases, and consequently, the gas inside the balloon expands.

The pressure at 99 feet is approximately 4 atmospheres (3 atmospheres from the water pressure plus 1 atmosphere from the air). The pressure at 33 feet is about 2 atmospheres (1 atmosphere from the air plus 1 atmosphere from the water).

Using Boyle's Law: [ P_1 \times V_1 = P_2 \times V_2 ]

Where

• ( P_1 ) and ( V_1 ) are the initial pressure and volume at 99 feet,
• ( P_2 ) and