A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4cm and its height is 25 cm. If thickness of the metal is 8mm everywhere, calculatd the volume of metal in the cylinder
704
To find the volume of the metal in the cylinder, we need to subtract the volume of the hollow space inside the cylinder from the total volume of the cylinder.
1. Calculate the internal radius of the cylinder:
The internal diameter is given as 10.4 cm. To find the internal radius, divide the diameter by 2:
Internal radius = Internal diameter / 2 = 10.4 cm / 2 = 5.2 cm
2. Calculate the external radius of the cylinder:
Since the thickness of the metal is 8 mm on all sides, we need to add the thickness to the internal radius to get the external radius:
External radius = Internal radius + Thickness = 5.2 cm + 0.8 cm (converting 8 mm to cm) = 6 cm
3. Calculate the volume of the hollow space inside the cylinder:
The formula for the volume of a cylinder is V = πr^2h.
The hollow space inside the cylinder can be considered as another smaller cylinder with the same height but a different radius.
So, the volume of the hollow space is V_inner = π(internal radius)^2h = π(5.2 cm)^2 * 25 cm
4. Calculate the volume of the entire cylinder:
The volume of the entire cylinder is V_total = π(external radius)^2h = π(6 cm)^2 * 25 cm
5. Calculate the volume of the metal:
Since the metal forms the difference between the total volume and the hollow space volume, we can subtract the latter from the former:
V_metal = V_total - V_inner
Now, you can substitute the values and calculate the volume of the metal.
just figure the difference between the outside and inside volumes:
V = πr^2 h, so you want
π(10.4+0.8)^2(25) - π(10.4^2)(25)
= 25π(11.2^2-10.4^2)
= 432π