A hollow rubber ball with a diameter of 5.57 cm and a mass of 38.9 g is cut in half to make a boat (in a bathtub) for American pennies made after 1982. The mass and volume of an American penny made after 1982 are 2.5 g and 0.36 cm3. How many pennies can be placed in the boat without sinking it?

To determine the number of pennies that can be placed in the boat without sinking it, we need to consider the buoyancy and weight of the boat and the weight of the pennies.

First, let's calculate the volume of the hollow rubber ball (the boat) using its diameter. The formula for the volume of a sphere is:

Volume = (4/3) * π * r^3

Given that the diameter of the rubber ball is 5.57 cm, we can find its radius (r) by dividing the diameter by 2:

r = 5.57 cm / 2 = 2.785 cm

Now, we can calculate the volume of the boat using the formula:

Volume = (4/3) * π * (2.785 cm)^3 = 69.523 cm^3

Since the boat is hollow, it does not have any mass of its own. The total weight of the boat will be equal to the total weight of the pennies it can hold without sinking.

Now, let's calculate the number of pennies that can be placed in the boat. Given that each penny has a mass of 2.5 g and a volume of 0.36 cm^3:

Number of pennies = (Total weight the boat can hold) / (Mass of each penny)

First, we need to calculate the total weight the boat can hold. We know that the total weight of the boat is the same as the weight of the pennies it can hold without sinking.

Total weight the boat can hold = Weight of the boat + Weight of the pennies

The weight of the boat can be calculated using its mass (38.9 g) and the acceleration due to gravity (typically 9.8 m/s^2). However, we must convert the mass of the boat to kilograms:

Weight of the boat = Mass of the boat * Acceleration due to gravity

Weight of the boat = 38.9 g * (1 kg / 1000 g) * 9.8 m/s^2 = 0.0389 kg * 9.8 m/s^2 = 0.38062 N

Now, we can calculate the number of pennies:

Number of pennies = (Total weight the boat can hold) / (Mass of each penny)

Number of pennies = 0.38062 N / 2.5 g = (0.38062 N) / (2.5 g * (1 kg / 1000 g)) = (0.38062 N) / (0.0025 kg)

Number of pennies = 152.248 pennies

Therefore, the boat can hold 152 pennies without sinking.