A rectangular tube is being made. The outside of the tube is 15 cm long, 6 cm tall and 10 cm wide. The hollow core is in the middle and runs the length of the tube. How much metal is needed to make this tude?
tube wall thickness?
the volume of metal is just the cross-section area times the length.
If the walls have thickness x then the cross-section area of the metal is just
6*10 - (6-2x)(10-2x)
To find the amount of metal needed to make the tube, we need to calculate the surface area of the outer surface and then subtract the surface area of the hollow core.
- Step 1: Calculate the surface area of the outer surface of the tube.
The outer surface of the tube consists of six rectangular faces: two large faces (front and back), and four smaller faces (sides and top/bottom).
The front and back face each have dimensions of 15 cm by 6 cm, which gives a surface area of 15 cm * 6 cm = 90 cm^2 each.
The four smaller faces each have dimensions of 15 cm by 10 cm, which gives a surface area of 15 cm * 10 cm = 150 cm^2 each.
So the total surface area of the outer surface is (2 * 90 cm^2) + (4 * 150 cm^2) = 780 cm^2.
- Step 2: Calculate the surface area of the hollow core.
The hollow core is like a rectangular box with inner dimensions equal to the outer dimensions of the tube. So the surface area is the same as the outer surface area.
- Step 3: Calculate the amount of metal needed.
The amount of metal needed is the difference between the surface area of the outer surface and the surface area of the hollow core: 780 cm^2 - 780 cm^2 = 0 cm^2.
Therefore, no additional metal is needed to make the tube as the hollow core will be created by removing the specified volume of material from the solid block.