Find the density of a 4.2- kg solid cylinder that is 13 cm tall with a radius of 5.0 cm.
D=m/V=m/π•R^2•h
I am lost on the numbers to plug into this one please help
D=m/V=m/π•R^2•h =4.2/3.14•(0.05)^2•0.13=4113.5kg/m^3
To find the density of the solid cylinder, you need to know its mass and its volume. The formula for density is given by:
Density = Mass / Volume
1. First, let's find the volume of the solid cylinder. The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h
Where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the cylinder
- h is the height of the cylinder
Plugging in the given values:
Volume = π * (5.0 cm)^2 * 13 cm
2. Since the radius is given in centimeters, the volume will be in cubic centimeters (cm³). However, it's more convenient to work with the SI unit, cubic meters (m³). Therefore, we need to convert the volume to cubic meters. Since 1 m³ = 1,000,000 cm³, we can divide the volume by 1,000,000 to convert it to cubic meters.
Volume = (π * (5.0 cm)^2 * 13 cm) / 1,000,000 m³
3. Evaluate the value of the volume, remembering to square the radius before multiplying:
Volume ≈ (3.14159 * (5.0 cm)^2 * 13 cm) / 1,000,000 m³
4. After calculating the value for the volume, we can move on to calculating the density:
Density = Mass / Volume
Plugging in the given mass:
Density = 4.2 kg / Volume
5. Finally, divide the mass by the calculated volume to find the density:
Density ≈ 4.2 kg / [(3.14159 * (5.0 cm)^2 * 13 cm) / 1,000,000 m³]
Calculating this expression will give you the density of the solid cylinder.