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?
The boat sinks when the weight of a hemisphere of displaced water equals the weight of the hemisphere ball AND the pennies inside.
Write that as an equation and solve for the mass of pennies.
Divide that by mass of a penny to get the number of pennies. The volume of the pennies doesn't matter, because is is the hemispherical ball that displaces the water. ,
I don't understand how to solve :(
To find out how many pennies can be placed in the boat without sinking it, we need to compare the total mass of the boat to the total mass of the pennies that can be placed in it.
First, let's calculate the mass of the boat. We know that the mass of the hollow rubber ball is 38.9 g. However, the ball has been cut in half to make the boat. So, the mass of the boat will be half the mass of the ball.
Mass of the boat = (Mass of the ball) / 2
Mass of the boat = 38.9 g / 2
Mass of the boat = 19.45 g
Now, let's calculate the mass of a single penny made after 1982, which we know is 2.5 g.
Next, we can determine how many pennies we can fit in the boat without sinking it by dividing the mass of the boat by the mass of a single penny.
Number of pennies = (Mass of the boat) / (Mass of a single penny)
Number of pennies = 19.45 g / 2.5 g
Number of pennies ≈ 7.78
Since we can't have a fraction of a penny, we need to round down to the nearest whole number. Therefore, we can place a maximum of 7 pennies in the boat without sinking it.