A hollow metal pipe has an external radius of 5cm and an internal radius of of 4.5cm. If the pipe is 1m long, find the volume of the metal used to make the pipe.
I am really confused how to begin to solve this, can someone help please?
Do you subtract it.
Take the total volume of the pipe (the full radius of 5cm) and you will have to find the volume of the smaller pipe size with radius 4.5 cm
Volume of metal = total volume of large pipe - (volume of internal pipe with radius 4.5 cm)
So in conclusion... find both volumes then take the smaller volume away from the larger one :)
To find the volume of the metal used to make the pipe, we need to subtract the volume of the hollow space from the volume of the cylinder.
First, let's calculate the volume of the hollow space:
V_hollow = π * (r_external^2 - r_internal^2) * h
Where:
- r_external is the external radius of the pipe (5 cm)
- r_internal is the internal radius of the pipe (4.5 cm)
- h is the height of the pipe (1 m = 100 cm)
Substituting the given values into the formula:
V_hollow = π * (5^2 - 4.5^2) * 100
V_hollow = π * (25 - 20.25) * 100
V_hollow = π * 4.75 * 100
Now, let's calculate the volume of the cylinder (including the hollow space):
V_cylinder = π * r_external^2 * h
Substituting the given values into the formula:
V_cylinder = π * 5^2 * 100
V_cylinder = π * 25 * 100
Finally, to find the volume of the metal used to make the pipe, we subtract the volume of the hollow space from the volume of the cylinder:
V_metal = V_cylinder - V_hollow
V_metal = (π * 25 * 100) - (π * 4.75 * 100)
V_metal = π * (25 - 4.75) * 100
V_metal = π * 20.25 * 100
So, the volume of the metal used to make the pipe is π * 20.25 * 100 cubic centimeters.
Of course! I'd be happy to help you with this problem.
To find the volume of the metal used to make the pipe, we can subtract the volume of the hollow part (the inner cylinder) from the volume of the entire pipe (the outer cylinder).
To begin solving this problem, let's first find the volumes of the inner and outer cylinders separately.
The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
For the inner cylinder:
Radius (r1) = 4.5 cm = 0.045 m (since 1 cm = 0.01 m)
Height (h) = 1 m
Volume of the inner cylinder (V1) = πr1^2h
For the outer cylinder:
Radius (r2) = 5 cm = 0.05 m
Height (h) = 1 m
Volume of the outer cylinder (V2) = πr2^2h
Now that you have the formulas for the volumes of the inner and outer cylinders, you can find their respective volumes by substituting the given values and using a calculator to evaluate the expressions.
Once you have both volumes, you can find the volume of the metal used to make the pipe by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
Volume of the metal used to make the pipe = V2 - V1
I hope this helps you get started with solving the problem! Let me know if you need any further assistance.