Help Calculating Surface Area of a Cylinder with a Slit

I need help calculating the surface area of a cylinder with a rectangular slit cut through one end.
Approximate measurements
Length of cylinder is 10mm,
diameter= 6mm
height of slit: 2.5mm
width of slit=1.5mm
Slit is cut through the middle of the top face of the cylinder. 

Geometry Area Algebraic Geometry
Samikai12 Samikai12
8
Matchmaticians Help Calculating Surface Area of a Cylinder with a Slit File #1 File #1 (jpg)
Matchmaticians Help Calculating Surface Area of a Cylinder with a Slit File #2 File #2 (jpg)
Matchmaticians Help Calculating Surface Area of a Cylinder with a Slit File #3 File #3 (jpg)
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  • Savionf Savionf
    0

    Is 1.5mm the length of the curved arc, or it is the length of the straight line segment from one end to the other end of the slit?

    • Samikai12 Samikai12
      0

      If you look at picture #3 and imagine X and Y axis , 1.5 mm is the length from the left side of the slit to the right side, measured with a calipher, through the Y axis. 2.5 mm is the length of the Slit/ depth.

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Kav10 Kav10
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  • Samikai12 Samikai12
    0

    Thanks for your help Kav10. I don't understand this part. s=rt is the equation for arc length. but what we need here is the surface area of this piece with arc length s. I'd be happy to tip if you can help me with this.

    • Kav10 Kav10
      0

      Sure. See the two lines after that line (s=rt). I explained that the surface area for those two arcs, is a rectangular, so the surface is calculated accordingly. The two surface areas with arcs equal to rectangular if opened (lay on a flat surface, on the arc side), so we calculate the rectangular area. It is like a curved paper, but if you lay the paper on the floor, it is a rectangular. Let me know if it is still not clear.

  • Samikai12 Samikai12
    0

    Cool, you are awesome. Thanks

    • Kav10 Kav10
      0

      You are welcome. Thanks.

  • Samikai12 Samikai12
    0

    Hey I was thinking about this last night. for the last term of the equation. about the 2 inner rectangles in the slit. We had 2x2.5mmx6mm; however it wouldn't be 6mm though, because the length of the rectangle don't pass through the center of the cylinder, they are a little less because of the area that is cut out. right? to calculate the length of the rectangle we would need to use the formula for arclength again and find the d based on the complementary angle to the one we found first?

    • Kav10 Kav10
      0

      Hey. You are right, but I think that would be very small, because of the ratio of the slit opening width to the whole diameter of the cylinder. I would say it probably will change the total surface area by less than 1%. If you want to be more precise, yes, it should be calculated separately. Let me know if you’d need help with that.

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