8th Grade Math Lesson

Volumes of Cylinders, Cones, and Spheres

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Grade 8 honorsBTC Style / Thinking Classrooms50 min

Learning Objective

Students will calculate the volume of cylinders, cones, and spheres using the formulas $V = π r^{2} h$ , $V = \frac{1}{3} π r^{2} h$ , and $V = \frac{4}{3} π r^{3}$ , and apply these formulas to composite and comparison problems.

Lesson Overview

Students progress from identifying radius and height in labeled diagrams to applying all three volume formulas, then comparing and combining solids in multi-step problems. Each task changes exactly one variable — formula, given information, or complexity layer.

Materials

Vertical whiteboards or chart paper
Dry-erase markers
Basic calculator or phone calculator

Scaffolded Task Progression

1Task 1

Find the volume of the cylinder below. Leave your answer in terms of $\pi$. ```solid {"figureType":"solid","solid":"cylinder","radius":3,"height":8,"labels":{"radius":"3 cm","height":"8 cm"},"title":"Cylinder"} ```

2Task 2

Find the volume of the cylinder below. The diameter is given. Leave your answer in terms of $\pi$. ```solid {"figureType":"solid","solid":"cylinder","radius":5,"height":6,"labels":{"radius":"d = 10 cm","height":"6 cm"},"title":"Cylinder"} ```

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