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Surface Area of Cylinders

Surface Area of Cylinders
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2018-12-15 03:01
Solid GeometryGeometric Construction
This example demonstrates the calculation of the surface area of cylinders. Key mathematical concepts include the geometric properties and area formulas of cylinders. Using GeoGebra commands such as Zip, Point, and Segment, users can dynamically adjust the radius and height of the cylinder to observe changes in the surface area. Suitable for middle school and above students learning geometry and area calculation.

GeoGebra Commands & Parameters

  1. Zip((A, sliderYval), A, validXvals) → sliderPoints
  2. Point(sliderPoints) → S
  3. IndexOf(x(S), validXvals) → currRow
  4. Join({Sequence["white", i, 1, currRow - 1], {"#fff59d"}, Sequence["white", i, currRow + 1, Max[13, maxRadius + 1]]}) → RowColours
  5. Sequence(Sequence[(((("\cellcolor{" * Element[RowColours, j]) * "}{") * Element[tblVals, i, j]) * "}"), i, 1, 3], j, 1, maxRow) → ListData
  6. Join({ListHeader, ListData}) → FullList
  7. TableText(FullList, "|111_111111111111l") → displayTbl
  8. LaTeX("\text{\textbf{Instructions: }Move the slider to change the radius of the cylinder.}") → SpecInstruc
  9. Element(First[sliderPoints], 1) → sliderEnd
  10. Segment(sliderStart, sliderEnd) → mySlider
  11. TableText({{LaTeX["\text{Radius =}"], currRadius}, {LaTeX["\text{Height =}"], height}, {LaTeX["\text{Volume =}"], fixedVolume}, {LaTeX["\text{Surface Area =}"], currSA}}, "|101 _1000 r") → currStatsDisp
  12. Cylinder(Circle[(0, 0, -25), currRadius, xOyPlane], height) → a_2, a_2, a_3
  13. LaTeX("\text{\textbf{Question: }A cylinder has a fixed volume of 400. As the radius changes, what happens \\to the height and the surface area? What are the dimensions of the cylinder when the \\surface area is a minimum?}") → MainInstruc