A spherical bass has a diameter of 1.00 inch and a mass of 2.00 grams. Will the ball float or sink water? Remember that if the ball's density if greater than 1.00 g/mL the density of water, the ball will sink. Also remember to use dimensional analysis.
Convert 1" to cm
1 in x 2.54 cm/in = 2.54 cm
Volume sphere = (4/3)*pi*r^3
Then density = mass/volume = ? and compare with 1.00 g/cc.
This would be the correct answer I was looking for.
Mass 2.00 Grams
Volume sphere = (4/3)*pi*r^3
Find radius first
1.00/2= 0.500in/2.54cm/1in ( the inches cancels out your left with 1.27 cm as the radius.
Volume of a sphere
(4/3)(3.14)(1.27)^3=8.58
Density = 2.00g/8.58cm^3= 0.233 g/cm^3
Ans 0.233 g/cm^3(its okay a lot of people make this mistake all the time not converting there units). your welcome.
To determine whether the ball will float or sink in water, we need to compare its density with the density of water. Density is defined as mass per unit volume.
Step 1: Find the volume of the spherical ball.
The volume of a sphere can be calculated using the formula:
V = (4/3)πr^3
where V is the volume and r is the radius of the sphere.
Given that the diameter of the ball is 1.00 inch, we can find the radius (r) by dividing the diameter by 2:
r = 1.00 inch / 2 = 0.50 inch
Step 2: Convert the radius to a consistent unit of measurement.
Since we want to use dimensional analysis, we need to convert the radius from inches to centimeters. There are 2.54 centimeters in an inch, so:
r = 0.50 inch * 2.54 cm/inch = 1.27 cm
Step 3: Calculate the volume of the sphere.
V = (4/3)π(1.27 cm)^3
V ≈ 8.47 cm^3
Step 4: Convert the mass to grams.
The given mass of the ball is already in grams, so there is no need for conversion.
Step 5: Calculate the density of the ball.
Density (ρ) is calculated by dividing the mass (m) by the volume (V):
ρ = m/V
Given that the mass of the ball is 2.00 grams and the volume is 8.47 cm^3, we can plug these values into the equation:
ρ = 2.00 g / 8.47 cm^3
ρ ≈ 0.236 g/cm^3
Step 6: Compare the density of the ball with the density of water.
The density of water is approximately 1.00 g/mL or 1.00 g/cm^3.
Since the density of the ball (0.236 g/cm^3) is less than the density of water (1.00 g/cm^3), the ball will float in water.