A regulation baseball has mass 145 g and diameter 22.86 cm. Will this ball float
or sink in water?
Vsphere =
€
4
3π⋅r3
To determine whether the baseball will float or sink in water, we need to compare its density to the density of water.
The density of an object is calculated by dividing its mass by its volume. The volume of a sphere is given by the formula: V = (4/3)πr^3, where r is the radius of the sphere.
First, we need to convert the diameter of the baseball to radius by dividing it by 2.
Given:
Mass of the baseball (m) = 145 g
Diameter of the baseball (d) = 22.86 cm
Radius (r) = d/2 = 22.86/2 = 11.43 cm = 0.1143 m
Using the volume formula for a sphere, we can now calculate the volume of the baseball:
V = (4/3)πr^3 = (4/3)π(0.1143^3) = 0.008 meters cubed (rounded to three decimal places)
Now, we can calculate the density of the baseball:
Density of the baseball (ρ) = mass/volume
= 145 g / 0.008 m^3
= 18125 g/m^3 (rounded to three decimal places)
Next, we need to compare the density of the baseball to the density of water.
The density of water is approximately 1000 kg/m^3.
Since the density of the baseball is greater than the density of water (18125 g/m^3 > 1000 g/m^3), the baseball will sink in water.