组合体体积计算应用题
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本范例演示如何计算由两个长方体组成的空间模型体积。涉及的核心数学概念是组合体体积计算。作图要点包括使用Shuffle、Element、Textfield、Polygon、Corner、Translate、Circle、Intersect、Segment、Line、Midpoint、Text等GeoGebra命令和对象。适合4-5年级学生学习如何解决实际生活中的组合体体积问题。
GeoGebra 命令及参数
Shuffle(Sequence[5]) → randomList1, {1, 3, 4, 5, 2}Element(randomList1, Mod[countQuestion, Length[randomList1]] + 1) → randomNum1Shuffle(Sequence[1, Min[100 / randomNum1, randomNum1 + 5]]) → randomList2, {6, 1, 5, 2, 4, 3}Element(randomList2, Mod[countQuestion, Length[randomList2]] + 1) → randomNum2Shuffle(Sequence[1, Min[100 / ((randomNum1 * randomNum2)), randomNum1 + 5]]) → randomList4, {2, 5, 6, 4, 1, 3}Shuffle(Sequence[1, Min[100 / randomNum1, randomNum1 + 5]] \ {randomNum2}) → randomList3, {2, 1, 5, 4, 3}Element(randomList3, Mod[countQuestion, Length[randomList3]] + 1) → randomNum3Element(randomList4, Mod[countQuestion, Length[randomList4]] + 1) → randomNum4Shuffle(Sequence[1, Min[100 / ((randomNum1 * randomNum3)), randomNum1 + 5]] \ {randomNum4}) → randomList5, {1, 6, 3, 5, 4}Textfield(input1) → InputBox1Element(randomList5, Mod[countQuestion, Length[randomList5]] + 1) → randomNum5Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBoxCorner(5) → layoutAppSizeTextfield() → InputBox2Corner(5) → AppSizeTranslate(hguideline, Vector[(Vector[Corner[4], Corner[1]] / 500 * 24)]) → hguideline'Circle(A, 4) → cIntersect(c, xAxis) → B, CSegment(A, C) → fCircle(A, modelWidth1) → dIntersect(d, f, 1) → DCircle(C, modelH2) → eIntersect(e, eq1, 1) → ELine(A, eq1) → gLine(E, f) → hLine(D, eq1) → iIntersect(h, i) → FLine(C, G) → jCircle(C, modelL) → kIntersect(k, j, 2) → HLine(H, eq1) → lLine(E, j) → mIntersect(l, m) → ICircle(A, modelH1) → pIntersect(p, g, 1) → JLine(F, m) → nLine(I, f) → qIntersect(n, q) → KLine(J, f) → rIntersect(i, r) → LPolygon(F, E, I, K) → q1, f_1, e_1, i_1, k_1Polygon(F, D, C, E) → q2, f_2, d_1, c_1, e_2Polygon(C, H, I, E) → q3, c_2, h_1, i_2, e_3Line(J, c_2) → sTranslate(L, Vector[C, H]) → L'Translate(D, Vector[C, H]) → D'Polygon({D, D', L', L}) → q4Translate(L', Vector[D, A]) → L''Polygon({J, L, L', L''}) → q5Polygon({J, A, D, L}) → q6Midpoint(A, D) → MMidpoint(C, D) → NText(labelH2, Midpoint[h_1], true, true, 1, 1) → text4Text(labelW1, M, true, true, -1, -1) → text2Text(labelW2, N, true, true, -1, -1) → text3Text(labelH1, Midpoint[A, J], true, true, -1, 0) → text5Text(labelL, Midpoint[C, H], true, true, 1, -1) → text6Circle(D, HintH1) → tIntersect(t, i) → O, PLine(O, h) → aIntersect(a, g) → QPolygon(D, O, Q, A) → q1H, d_2, o, q_1, a_1Translate(O, Vector[D, D']) → O'Polygon(D, D', O', O) → q2H, d_3, d', o', o_1Translate(q5, Vector[J, Q]) → q3HTranslate(D, (0, HintH2)) → D'_{1}Translate(C, (0, HintH2)) → C'Polygon(D, C, C', D'_{1}) → q4H, d_4, c_3, c', d'_{1}Translate(H, (0, HintH2)) → H'Polygon(C, H, H', C') → q5H, c_4, h_2, h', bTranslate(F, Vector[F, D'_{1}]) → F'Translate(E, Vector[F, D'_{1}]) → E'Translate(I, Vector[F, D'_{1}]) → I'Translate(K, Vector[F, D'_{1}]) → K'Polygon(F', E', I', K') → q6H, f', e', i', k'
AI 绘图提示语参考
这是一个由两个右直角棱柱组成的复合体积模型。图形包含一个边界矩形,以及一些圆、线段和交点,用于表示体积计算。构造顺序包括随机选择尺寸,绘制边界矩形,创建圆和线段,计算交点,最后绘制一些平行四边形。图形可能用于教学演示,帮助学生理解复合体积的概念。
以上提示语为根据原始绘图命令整理而来,仅供参考。