$\textsf{SA =}$

$\bold\textsf{Fold / Unfold}$

#4D4D4D

$\text{Check}$

$\text{NEW CYLINDER}$

No selection allowed for all input boxes

Fix position and allow selection for all text objects

Empty all input boxes

Reset app

\text{Simplify your answer.}

#006758

#B00020

#252525

#757575

#949494

#E44461

#DA2570

#E66B9E

#3A6ED6

#5991FF

#008475

#0F8538

#00a83c

#5145A8

#6557D2

#8575FF

#903D14

#BD6C43

#C75000

#E07415

#eeeeee

#2E006758

#2EB00020

#DA2570

#3A6ED6

\textsf{\bold{\pi} units^2}

view

\text{Open net}

$\textsf{REPLACE VARIABLES}$

\textsf{Explore the surface area of the cylinder.}

wait = 1 (slider from 0 to 1)
showhint = false
heiHint = 2.12
countQuestion = 0
countQuestion_{1}: countQuestion
ListRadius_{1} = Sequence(5)
randomListRadius_{1} = Shuffle(ListRadius_{1})
randomRadius = Element(randomListRadius_{1}, Mod[countQuestion_{1}, Length[randomListRadius_{1}]] + 1)
ListHeights = Zip(If[Mod[kk, 3] ≟ 0, Sequence[1 / 3, 5, 1 / 3], If[Mod[kk, 2] ≟ 0, Sequence[1 / 2, 5, 1 / 2], Sequence[5]]], kk, randomListRadius_{1})
ListHeightsC: ListHeights(Mod[countQuestion, Length[ListHeights]] + 1)
randomListHeight_{1} = Shuffle(ListHeightsC)
randomHeight_{1}: (Element[randomListHeight_{1}, 1] * randomRadius)
hei_{1}: randomHeight_{1} / randomRadius
input1 = NaN
showCylHint: 0.2 ≤ heiHint / hei_{1} ≤ 3 ∧ showhint
InputBox1 = Textfield(input1)
correct2: ¬Defined[IndexOf["+", Text[InputBox1 + "", false]]]
hei2: randomHeight_{1}
expAns: ((2 * randomRadius) * hei2) + (2 * randomRadius^(2))
correct1: abs(input1 - expAns) ≤ 0.01
tCil2 = 0 (slider from 0 to 1, step 0.01)
randomListIncrement_{1} = Shuffle(Sequence[0.1, 2, 0.01])
BaseCenter_{1}: (0, 1, 0)
tCil_{1}: (-tCil2)
θCil_{1}: (pi * (1 - abs(tCil_{1})))
rCil_{1}: pi / θCil_{1}
randomList2 = Shuffle(Sequence[15])
randomList1 = Shuffle(Sequence[20])
randomNum2 = Element(randomList2, Mod[countQuestion, 15] + 1)
input2: NaN
randomNum1 = Element(randomList1, Mod[countQuestion, 20] + 1)
validate = false
showanswer = false
showsolution = false
tries = 0
countCorrect = 0
correct: correct1 ∧ correct2
showbuttons = true
typicalError1: 0
typicalError2: 0
showhinttypicalerror = false
labelBtnValidate: "\text{CHECK (" + (LaTeX[3 - tries]) + ")}"
helpTextHint: "\text{" + (LaTeX[If[showCylHint, "The surface area from your last answer built\\a new cylinder. See how it compares.", "Find the area of the rectangle.\\Then find the area of each of the circles."]]) + "}"
ϕCil_{1}: (abs(tCil_{1}) * pi / 2)
CC_{1}: (0, 0, hei_{1})
CE_{1} = If(abs(tCil_{1}) < 1, ((rCil_{1} * sin((-θCil_{1}))), ((rCil_{1} * (1 - cos((-θCil_{1})))) * cos(ϕCil_{1})) - (hei_{1} * sin(ϕCil_{1})), (hei_{1} * cos(ϕCil_{1})) + ((rCil_{1} * (1 - cos((-θCil_{1})))) * sin(ϕCil_{1}))), ((-pi), ((-hei_{1}) * sin(ϕCil_{1})), (hei_{1} * cos(ϕCil_{1}))))
CF_{1} = If(abs(tCil_{1}) < 1, ((rCil_{1} * sin(θCil_{1})), ((rCil_{1} * (1 - cos(θCil_{1}))) * cos(ϕCil_{1})) - (hei_{1} * sin(ϕCil_{1})), (hei_{1} * cos(ϕCil_{1})) + ((rCil_{1} * (1 - cos(θCil_{1}))) * sin(ϕCil_{1}))), (pi, ((-hei_{1}) * sin(ϕCil_{1})), (hei_{1} * cos(ϕCil_{1}))))
CG_{1} = If(abs(tCil_{1}) < 1, ((rCil_{1} * sin((-θCil_{1}))), ((rCil_{1} * (1 - cos((-θCil_{1})))) * cos(ϕCil_{1})), ((rCil_{1} * (1 - cos((-θCil_{1})))) * sin(ϕCil_{1}))), ((-pi), 0, 0))
CH_{1} = If(abs(tCil_{1}) < 1, ((rCil_{1} * sin(θCil_{1})), ((rCil_{1} * (1 - cos(θCil_{1}))) * cos(ϕCil_{1})), ((rCil_{1} * (1 - cos(θCil_{1}))) * sin(ϕCil_{1}))), (pi, 0, 0))
mCil_{1} = Segment(CE_{1}, CG_{1})
nCil_{1} = Segment(CF_{1}, CH_{1})
speed_{1} = 3
lCil_{1} = If(abs(tCil_{1}) < 1, CurveCartesian[(rCil_{1} * sin((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1}))), ((rCil_{1} * (1 - cos((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1})))) * cos(ϕCil_{1})), ((rCil_{1} * (1 - cos((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1})))) * sin(ϕCil_{1})), CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu, -1, 1], CurveCartesian[(pi * CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu), 0, 0, CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu, -1, 1])
TV_{1}: (2, -2, 2)
jCil_{1} = If(abs(tCil_{1}) < 1, CurveCartesian[(rCil_{1} * sin((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1}))), ((rCil_{1} * (1 - cos((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1})))) * cos(ϕCil_{1})) - (hei_{1} * sin(ϕCil_{1})), (hei_{1} * cos(ϕCil_{1})) + ((rCil_{1} * (1 - cos((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1})))) * sin(ϕCil_{1})), CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu, -1, 1], CurveCartesian[(pi * CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu), ((-hei_{1}) * sin(ϕCil_{1})), (hei_{1} * cos(ϕCil_{1})), CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu, -1, 1])
iCil_{1} = If(abs(tCil_{1}) < 1, Surface[(rCil_{1} * sin((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1}))), ((rCil_{1} * (1 - cos((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1})))) * cos(ϕCil_{1})) - (CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGv * sin(ϕCil_{1})), (CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGv * cos(ϕCil_{1})) + ((rCil_{1} * (1 - cos((CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu * θCil_{1})))) * sin(ϕCil_{1})), CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu, -1, 1, CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGv, 0, hei_{1}], Surface[(pi * CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu), ((-CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGv) * sin(ϕCil_{1})), (CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGv * cos(ϕCil_{1})), CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGu, -1, 1, CLIPBOARDmagicSTRINGCLIPBOARDmagicSTRINGv, 0, hei_{1}])
BaseCil2 = Circle(BaseCenter_{1}, 1, Vector[(0, 0, 1)])
segRad_{1} = Segment((0, 1, 0), (1, 1, 0))
unfoldedCilinder_{1} = Polygon({((-pi), 0, 0), (pi, 0, 0), (pi, (-hei_{1}), 0), ((-pi), (-hei_{1}), 0)})
labelRadius_{1}: "\textsf{" + (LaTeX[randomRadius]) + "}"
E_{1}: (0, 4, 0)
F_{1}: (0, 2.3, 0)
G_{1} = (-4, 2, 0)
H_{1} = (-3.3583487139075943, -0.4495427412317252, 0)
J_{1} = (2.404933095475027, 5.737861179470774)
L_{1} = Corner(5)
MoveGuideLines_{1} = (2.1206684278417285, 3.5771759730725914)
verticalGuideLine_{1}: x = x(MoveGuideLines_{1})
AppSize: (x(Corner[1, 5]) + x(CornerThreeD[-1, 9]), y(Corner[5]))
BaseCil = Circle(BaseCenter_{1}, 1, Vector[(0, 0, 1)])
TopCilFixed = Circle(Translate[BaseCenter_{1}, Vector[(0, 0, hei_{1})]], 1, Vector[(0, 0, 1)])
TopPoint = Rotate((0, 0, hei_{1}), (pi / 2 * tCil_{1}), Line[(1, 0, 0), (-1, 0, 0)])
u = Vector((0, cos((tCil_{1} * pi)), (-sin((tCil_{1} * pi)))))
TopPointC = Translate(TopPoint, u)
v = Vector((0, sin((tCil_{1} * pi)), cos((tCil_{1} * pi))))
TopCil = Circle(TopPointC, 1, v)
TopCil2: TopCil
f: y = y(MoveGuideLines_{1})
A = Corner(5)
textCountCorrect: "\text{Number correct: " + (LaTeX[countCorrect]) + " }"
baseHint: BaseCil
a, topHint, b = Cylinder(baseHint, heiHint)
topHint2: topHint
normView = (0.8572814316582401, -0.4751988572105508, -0.19812771900919046)
isTypicalError: ¬correct2
xFeedback: 16 + If[correct ∨ tries ≟ 3, -5, 149]
yfeedback: 213 + If[correct, 6, 1]
labelPos = Midpoint(CG_{1}, CE_{1})
view = Vector((1; (pi / 2 * tCil2); ((-pi)) / 2 + ((0.8 * pi / 2) * (1 - tCil2))))
labelHeight_{1}: "\textsf{" + (LaTeX[If[hei2 ≤ 9, "\phantom{0}", ""]]) + "" + (LaTeX[hei2]) + "}"
textHint: "\text{\bold\color{" + (LaTeX[colorOrange]) + "}{Hint}\\\\" + (LaTeX[If[showhinttypicalerror, helpTextHintTypicalError]]) + "" + (LaTeX[If[showhint ∧ showhinttypicalerror, "\\"]]) + "" + (LaTeX[If[showhint, helpTextHint]]) + "}"
textFeedback: "" + (LaTeX[If[correct, "$\text{✓ Correct}$", "$\text{✕ " + (If[tries < 3, "Try again", "Maybe next time"]) + "}$"]]) + ""
inputSaved: {NaN}
inputCurrent: {input1, If[correct2, 1, 0]}
enableBtnValidate: inputCurrent ≠ inputSaved ∧ inputCurrent ≟ RemoveUndefined[inputCurrent]
enableInput: tries < 3 ∧ (¬(validate ∧ correct))
layoutX: 16
layoutY: 210
f' = Translate(f, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)])
CentView: (tCil_{1} * ((0, 1, hei_{1} / 2) - (0, ((-hei_{1})) / 2, 0))) + (0, 1, hei_{1} / 2)
stage = 0
textSolution: "\textsf{SA}= 2 \pi \times \bold\textcolor{" + (LaTeX[colorBlue_{1}]) + "}{" + (LaTeX[randomRadius]) + "} \times \bold\textcolor{" + (LaTeX[colorPink_{1}]) + "}{" + (LaTeX[hei2]) + "} + 2 \pi \times \bold\textcolor{" + (LaTeX[colorBlue_{1}]) + "}{" + (LaTeX[randomRadius]) + "}^2 \\\textsf{SA}=" + (LaTeX[expAns]) + " \pi\text{ sq. units}"
showcyl: wait ≟ 1
speedWait: 20
TopPoint' = Rotate(TopPoint, 90°, TopPointC, v)
segRadTop = Segment(TopPoint', TopPointC)
text4 = Text(labelRadius_{1}, TopPointC + ((0.2 * tCil2), (0.5 * tCil2), (tCil2 * hei_{1}) + 1), true, true)
questiontext_{1}: "\textsf{Formula for Cylinder Surface Area (SA):}\\\\
\textsf{SA = \color{" + (LaTeX[colorPink_{1}]) + "}Lateral Surface Area \color{}}+ 2 \times \color{" + (LaTeX[colorBlue_{1}]) + "}\textsf{Base Area}\\
\textsf{SA = }\textcolor{" + (LaTeX[If[stage ≟ 1, colorPink_{1}, colorBlack]]) + "}{2 \pi " + (LaTeX[If[stage ≟ 2, (("\bold\textcolor{" * colorBlue_{1}) * "}")]]) + "r \times " + (LaTeX[If[stage ≟ 2, (("\bold\textcolor{" * colorPink_{1}) * "}")]]) + "h }+ 2 \times \textcolor{" + (LaTeX[If[stage ≟ 1, colorBlue_{1}, colorBlack]]) + "}{\pi " + (LaTeX[If[stage ≟ 2, (("\bold\textcolor{" * colorBlue_{1}) * "}")]]) + "{r}^2}\\" + (LaTeX[If[stage ≟ 2, textSolution, ""]]) + ""