Find the density of a 4.2- kg solid cylinder that is 13 cm tall with a radius of 5.0 cm.
Divide the mass (4200 g) by the volume of the cylinder, V.
V = pi*R^2*L
L = length in cm
R = radius in cm
M/V is the density in g/cm^3.
To find the density of the solid cylinder, we need to use the formula:
Density = Mass / Volume
Step 1: Find the volume of the cylinder
The volume of a cylinder is given by the formula:
Volume = π * (radius)^2 * height
Given that the radius of the cylinder is 5.0 cm and the height is 13 cm, we can substitute these values into the formula:
Volume = π * (5.0 cm)^2 * 13 cm.
Step 2: Calculate the volume of the cylinder
Using a calculator and the value of π (pi) as approximately 3.14159, we have:
Volume = 3.14159 * (5.0 cm)^2 * 13 cm
Volume ≈ 3.14159 * 25 cm^2 * 13 cm
Volume ≈ 1024.607 cm^3
Step 3: Calculate the density of the cylinder
The mass of the cylinder is given as 4.2 kg.
Density = Mass / Volume
Density = 4.2 kg / 1024.607 cm^3
To convert the volume from cm^3 to m^3, we need to divide by 1,000,000. So the volume becomes 0.001024607 m^3.
Density = 4.2 kg / 0.001024607 m^3
Using a calculator, we find:
Density ≈ 4103.143 kg/m^3
Therefore, the density of the 4.2 kg solid cylinder is approximately 4103.143 kg/m^3.