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Geometry Lesson

Unwrapping 3D Solids: Volume & Surface Area from Prisms to Spheres

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High SchoolThin-SlicingCCSS.MATH.CONTENT.HSG.GMD.A.1, CCSS.MATH.CONTENT.HSG.GMD.A.3, CCSS.MATH.CONTENT.HSG.MG.A.150 min
Learning Objective

Students will be able to calculate the volume and surface area of prisms, cylinders, pyramids, cones, and spheres, and apply these formulas to composite solids and real-world contexts.

Lesson Overview

Students progress from computing volume and surface area of familiar prisms, then systematically change one solid type at a time — cylinder, pyramid, cone, sphere — building formula intuition through discovery at vertical surfaces. The lesson culminates in composite solid problems.

Materials

  • Vertical whiteboards or large chart paper
  • Dry-erase markers (multiple colors)
  • Formula reference sheet (blank — students build it)
  • Random grouping cards

Scaffolded Task Progression

1Task 1
A rectangular prism (box) has a length of cm, width of cm, and height of cm.

Part A: Find the volume.

Part B: Find the surface area (the total area of all six faces).

*Hint: Draw and label each face.*
2Task 2
A triangular prism has a triangular base with base cm and height cm. The prism's length (depth) is cm.

Part A: Find the volume.

Part B: Find the surface area. (The two triangular faces + three rectangular faces.)

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