According to the rules of golf, a golf ball cannot weigh more than 45.97 grams, and it must be at least 4.267 cm in diameter. The volume of a sphere is (4/3)πr3, where r is the radius.
What is the density of a 45.67 g golf ball with a diameter of 4.267 cm?
Well, to calculate the density, we need to find the volume of the golf ball first. The formula for volume of a sphere is (4/3)πr³.
Given that the diameter is 4.267 cm, the radius would be half of that, which is 2.1335 cm.
Let's plug that into the formula:
Volume = (4/3)π(2.1335³)
Volume ≈ 38.19703 cm³
Now, we can calculate the density by dividing the mass by the volume:
Density = mass/volume
Density = 45.67 g / 38.19703 cm³
So, the density of the golf ball is approximately 1.195 g/cm³.
But you know, even with all these calculations, the real question is, can you tell the difference between a high-density golf ball and a low-density golf ball just by how far they fly? Because if you can, you might as well go play golf on the moon, where the low gravity will probably make even the heaviest golf balls feel like featherweights!
To find the density of a golf ball, we need to calculate its volume first.
Given:
- Weight of the golf ball (m) = 45.67 g
- Diameter of the golf ball (d) = 4.267 cm
Let's start by finding the radius (r) of the golf ball:
Since the diameter (d) is given, we can calculate the radius (r) as half of the diameter:
r = d/2
r = 4.267 cm / 2
r = 2.1335 cm
Next, we can calculate the volume (V) of the golf ball using the formula for the volume of a sphere:
V = (4/3)πr^3
= (4/3) * π * (2.1335 cm)^3
≈ 4.8514 cm^3
Now that we have the volume (V) and the weight (m) of the golf ball, we can calculate its density (ρ) using the formula:
ρ = m / V
= 45.67 g / 4.8514 cm^3
≈ 9.41 g/cm^3
Therefore, the density of the 45.67 g golf ball with a diameter of 4.267 cm is approximately 9.41 g/cm^3.
To find the density of a golf ball, we need to know its mass and volume. The mass is given as 45.67 grams, and the volume can be calculated using the formula for the volume of a sphere.
The first step is to find the radius of the golf ball. Since the diameter is given as 4.267 cm, the radius can be calculated by dividing the diameter by 2.
Radius = Diameter / 2
Radius = 4.267 cm / 2
Radius = 2.1335 cm
Next, we can calculate the volume of the golf ball using the formula for the volume of a sphere.
Volume = (4/3) * π * r^3
Volume = (4/3) * 3.14159 * (2.1335 cm)^3
Volume ≈ 4.0004 * 3.14159 * (9.158336 cm^3)
Volume ≈ 114.7105 cm^3
Now that we have both the mass (45.67 grams) and the volume (114.7105 cm^3) of the golf ball, we can calculate its density.
Density = Mass / Volume
Density = 45.67 g / 114.7105 cm^3
Density ≈ 0.3987 g/cm^3
Therefore, the density of the 45.67 g golf ball with a diameter of 4.267 cm is approximately 0.3987 g/cm^3.
radius (r) is equal to half of the diameter
so the volume of the ball is ... (4/3) π (d/2)^3
divide the mass (weight) by the volume to find the density
... there are only four significant figures in the answer