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Unit 12: Surface Area Sketch of Solids

Unit 12: Surface Area Sketch of Solids
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2016-04-22 03:14
PolygonSolid GeometryGeometric ConstructionGraphing
This GeoGebra example presents a composite sketch of multiple 3D solids—including a cube, prism, pyramid, cylinder, sphere, and cone—to illustrate the concept of surface area. The core mathematical focus is solid geometry, specifically calculating and visualizing the surface areas of various polyhedra and curved solids. The construction uses GeoGebra commands such as Point, Cube, Prism, Pyramid, Cylinder, Sphere, and Cone to generate the solids, with named faces (e.g., faceGHIJ, faceOPQ) and edges (e.g., edgeGJ, edgeGH) to highlight individual surfaces, and text objects for labels. This resource is ideal for middle or high school students learning about surface area in geometry, serving as a visual aid for classroom demonstrations or independent exploration to understand how surface areas are composed and computed.

GeoGebra Commands & Parameters

  1. Point(Circle[H, Distance[G, H], Segment[G, H]]) → I
  2. Cube(G, H, I) → b, J, faceIJNM, faceKLMN, edgeGJ, edgeGH, edgeHI, edgeIJ, edgeGK, edgeJN, edgeKN, edgeKL, K, edgeHL, edgeLM, edgeIM, edgeMN, L, M, N, faceGHIJ, faceGJNK, faceGHLK, faceHIML
  3. Prism(O, P, Q, T) → c, R, edgeOQ, edgeOT, edgePR, edgeQS, edgeRT, edgeRS, edgeST, S, faceOPQ, faceOPRT, facePQSR, faceOQST, faceRST, edgeOP, edgePQ
  4. Pyramid(U, V, W, Z) → d, faceUVW, edgeWZ, faceUVZ, faceVWZ, faceUWZ, edgeUV, edgeVW, edgeUW, edgeUZ, edgeVZ
  5. Prism(A, B, C, D, B_1) → a, E, edgeAB, edgeBC, edgeCD, edgeAD, edge1, edgeBE, edgeCF, edge2, edge3, edgeEF, F, edge5, edge4, A_1, faceABCD, face1, faceBCFE, face3, face2, face4
  6. Cylinder(C_1, D_1, 1) → e, f, g, h
  7. Sphere(E_1, 2) → i
  8. Cone(F_1, G_1, 2) → j, k, l
  9. Pyramid(H_1, I_1, J_1, K_1, L_1) → m, face9, edge8, edge10, edge12, edge13, face5, face7, face8, face6, edge6, edge9, edge11, edge7