A piece of pipe has an outer radius of 4.6 cm, an inner radius of 2.8 cm, and length of 35 cm. What is the mass of this pipe? Assume its density is 8.3 g/cm3. Answer in units of k
where are the answers
V=V1-V2= πR²h-πr² h=πh(R²-r²)
m=ρV=ρπh(R²-r²)
To find the mass of the pipe, we need to calculate its volume and then multiply it by its density.
1. Start by finding the volume of the pipe. The pipe is essentially a cylinder with hollowed-out section. So, we need to find the volume of the cylinder and subtract the volume of the hollowed-out section.
2. The volume of the cylinder can be calculated using the formula: V = π * r^2 * h, where V is the volume, π is a mathematical constant (approximately 3.14159), r is the radius, and h is the height or length of the cylinder.
3. Substitute the values into the formula: V_cylinder = 3.14159 * (4.6 cm)^2 * 35 cm.
4. Next, we need to find the volume of the hollowed-out section. The volume of a hollow cylinder can be calculated using the formula: V = π * (R^2 - r^2) * h, where V is the volume, π is the mathematical constant, R is the outer radius, r is the inner radius, and h is the height or length of the cylinder.
5. Substitute the values into the formula: V_hollowed_out = 3.14159 * ((4.6 cm)^2 - (2.8 cm)^2) * 35 cm.
6. Now, subtract the volume of the hollowed-out section from the volume of the whole cylinder to find the volume of the pipe: V_pipe = V_cylinder - V_hollowed_out.
7. Finally, calculate the mass of the pipe by multiplying the volume by its density: mass = V_pipe * density.
Let's calculate the mass of the pipe step-by-step:
V_cylinder = 3.14159 * (4.6 cm)^2 * 35 cm
V_hollowed_out = 3.14159 * ((4.6 cm)^2 - (2.8 cm)^2) * 35 cm
V_pipe = V_cylinder - V_hollowed_out
mass = V_pipe * density
Substituting the values and performing the calculations will give us the final answer.
To find the mass of the pipe, we need to calculate its volume first. The volume of the pipe can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
The volume of a cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height (or length in this case) of the cylinder.
Let's begin by calculating the volume of the outer cylinder:
V_outer = π * (4.6 cm)^2 * 35 cm
Next, we'll calculate the volume of the inner cylinder:
V_inner = π * (2.8 cm)^2 * 35 cm
Now, we can subtract the volume of the inner cylinder from the volume of the outer cylinder to find the volume of the pipe itself:
V_pipe = V_outer - V_inner
Once we have the volume of the pipe, we can find its mass by multiplying it by the density of the material:
Mass = V_pipe * density
Substituting the given values, the final calculation becomes:
Mass = V_pipe * 8.3 g/cm^3
Now, let's calculate the values and find the mass of the pipe:
V_outer = π * (4.6 cm)^2 * 35 cm
V_inner = π * (2.8 cm)^2 * 35 cm
V_pipe = V_outer - V_inner
Mass = V_pipe * 8.3 g/cm^3
Calculating each step:
V_outer = (3.14) * (4.6 cm)^2 * 35 cm ≈ 692.62 cm^3
V_inner = (3.14) * (2.8 cm)^2 * 35 cm ≈ 77.44 cm^3
V_pipe = 692.62 cm^3 - 77.44 cm^3 ≈ 615.18 cm^3
Mass = 615.18 cm^3 * 8.3 g/cm^3 ≈ 5,106.26 g
Finally, converting the mass to kilograms by dividing by 1000:
Mass = 5,106.26 g ÷ 1000 ≈ 5.11 kg
Therefore, the mass of the pipe is approximately 5.11 kg.