长方锥体的表面展开图
几何画板及绘图内容加载中,请稍等……
本GeoGebra范例用于探索长方锥体的表面展开图及其表面积公式。它涉及立体几何中的核心概念,如锥体的表面积计算。通过使用GeoGebra命令,如Line(线)、Circle(圆)、Intersect(交点)、Vector(向量)等,可以动态展示锥体的构造过程。适合初中及以上学生学习锥体的相关知识。
GeoGebra 命令及参数
Line(J, K) → hCircle(J, width) → gIntersect(g, h, 1) → MVector(J, M) → wTranslate(A, Vector[w / 2]) → CDilate(I, length, H) → LVector(H, L) → vTranslate(C, v) → DMidpoint(C, D) → Q_1Translate(A, v) → BMidpoint(A, B) → YLine(Y, Q_1) → g_1Midpoint(C, B) → NCircle(Q_1, N) → k_1Intersect(k_1, g_1, 2) → V_1Dilate(F, height, E) → GVector(E, G) → uTranslate(N, u) → OPolygon(A, B, D, C) → P, a, b, d, cPolygon(O, C, D) → Q, d_1, o, c_1Polygon(O, A, C) → R, c_2, o_1, a_1Polygon(O, D, B) → S, b_1, o_2, d_2Polygon(O, A, B) → T, b_2, o_3, a_2Midpoint(B, D) → USegment(O, N) → eSegment(O, U) → fMidpoint(O, U) → WMidpoint(O, N) → VIf(height ≤ 5, C) → ZSegment(Z, O) → iSegment(Z, A) → jLine(N, U) → kIntersect(k, c) → E_1OrthogonalLine(E_1, k) → lOrthogonalLine(U, k) → mCircle(E_1, width / 2) → pIntersect(p, l, 2) → F_1OrthogonalLine(F_1, l) → nIntersect(p, l, 1) → G_1OrthogonalLine(G_1, l) → qIntersect(m, n) → H_1Intersect(m, q) → I_1Midpoint(F_1, H_1) → J_1Midpoint(I_1, G_1) → K_1Line(J_1, K_1) → rCircle(E_1, A1) → sMidpoint(H_1, I_1) → L_1Circle(U, A1) → tIntersect(s, k, 1) → M_1Intersect(t, k, 2) → N_1Circle(J_1, A2) → e_1Circle(K_1, A2) → f_1Intersect(e_1, r, 1) → O_1Intersect(f_1, r, 2) → P_1Vector(O, M_1) → z_1Vector(O, N_1) → i_1Midpoint(Q_1, N) → R_1Midpoint(Y, N) → S_1Circle(S_1, O) → q_1Intersect(q_1, g_1, 1) → T_1Vector(T_1, P_1) → u_1Vector(O, T_1) → w_1Vector(A, G_1) → l_1Vector(B, I_1) → n_1Vector(D, H_1) → r_1Circle(V_1, O) → h_1Vector(C, F_1) → s_1Intersect(h_1, g_1, 2) → U_1Vector(O, U_1) → zVector(U_1, O_1) → j_1CircleArc(S_1, O, T_1) → p_1CircleArc(V_1, U_1, O) → t_1CircumcircleArc(M_1, O, N_1) → e_2Center(e_2) → W_1Translate(O, Vector[w_1 * m_1]) → O'Translate(O, Vector[z_1 * (m_1 - 1)]) → O'_1Translate(O, Vector[z * (m_1 - 2)]) → O'_2Translate(O, Vector[i_1 * (m_1 - 3)]) → O'_3Translate(T_1, Vector[u_1 * (m_1 - 4)]) → Z_1Translate(U_1, Vector[j_1 * (m_1 - 4)]) → A_2Ray(S_1, O') → f_2Intersect(p_1, f_2, 1) → C_2If(m_1 ≤ 0, O, If[m_1 < 1, C_2, If[m_1 < 4, T_1, If[m_1 < 5, Z_1, P_1]]]) → B_2Ray(W_1, O'_1) → g_2Intersect(e_2, g_2, 1) → D_2If(m_1 ≤ 1, O, If[m_1 < 2, D_2, M_1]) → E_2Ray(W_1, O'_3) → h_2Intersect(e_2, h_2, 1) → F_2If(m_1 ≤ 3, O, If[m_1 < 4, F_2, N_1]) → G_2Ray(V_1, O'_2) → i_2Intersect(t_1, i_2, 1) → H_2If(m_1 ≤ 2, O, If[m_1 < 3, H_2, If[m_1 < 4, U_1, If[m_1 < 5, A_2, O_1]]]) → I_2Translate(A, Vector[l_1 * (m_1 - 4)]) → A'Translate(B, Vector[n_1 * (m_1 - 4)]) → B'Translate(D, Vector[r_1 * (m_1 - 4)]) → D'Translate(C, Vector[s_1 * (m_1 - 4)]) → C'If(m_1 ≤ 4, A, If[m_1 < 5, A', G_1]) → J_2If(m_1 ≤ 4, C, If[m_1 < 5, C', F_1]) → K_2If(m_1 ≤ 4, D, If[m_1 < 5, D', H_1]) → L_2If(m_1 ≤ 4, B, If[m_1 < 5, B', I_1]) → M_2Polygon(E_2, K_2, J_2) → poly1, j_2, e_3, k_2Polygon(J_2, M_2, B_2) → poly2, b_3, j_3, m_2Polygon(M_2, G_2, L_2) → poly3, l_2, m_3, g_3Polygon(L_2, I_2, K_2) → poly4, k_3, l_3, i_3Polygon(K_2, J_2, M_2, L_2) → poly5, k_4, j_4, m_4, l_4Segment(U, G_2) → n_2Midpoint(U, G_2) → N_2Midpoint(O, U) → O_2Vector(P_2, N_2) → u_2Vector(P_2, O_2) → v_2Segment(N, O) → p_2Midpoint(O, N) → Q_2Segment(A, O) → q_2Segment(B, O) → r_2Segment(D, O) → t_2Segment(C, O) → a_3Segment(U, O) → c_3Midpoint(K_2, L_2) → R_2Segment(R_2, A_2) → d_3Midpoint(Q_2, I_2) → S_2Vector(T_2, S_2) → w_2Segment(J_2, K_2) → f_3