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Mathematics · Grade 8

Volume of Cylinders, Cones and Spheres

Learners extend base-times-height to cylinders, discover that a cone holds one third of the matching cylinder, and find sphere volumes with the 1 : 2 : 3 relationship among a cone, a sphere and a cylinder. They give exact answers in terms of π and approximate answers with π ≈ 3.14, then work backward to missing heights and radii (using square and cube roots) and find the volume of composite solids in real situations.

  • 4 lessons
  • About 90 minutes
  • Volume of cylinders, cones and spheres check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, match pairs, type a number, put in order and true or false
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What learners will discover

  • Find the volume of a cylinder with V = πr^2^h, exactly in terms of π and approximately with π ≈ 3.14.
  • Find the volume of a cone with V = [[1/3]]πr^2^h and explain its relationship to a cylinder with the same base and height.
  • Find the volume of a sphere or hemisphere with V = [[4/3]]πr^3^ and relate the volumes of a cone, a sphere and a cylinder.
  • Solve real-world and mathematical problems with these volumes, including finding a missing dimension and the volume of composite solids.

Lessons

  1. Cylinders: base area times height 9 steps5 practiceabout 22 min
  2. Cones: one third of a cylinder 9 steps6 practiceabout 22 min
  3. Spheres and the 1 : 2 : 3 relationship 8 steps5 practiceabout 22 min
  4. Missing dimensions and composite solids 9 steps5 practiceabout 24 min
  5. Volume of cylinders, cones and spheres check 10 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Algebra BalanceKeep the scale level and the equation true, step by step.
  • Function FactoryFeed the machine, crack its rule and predict what comes out.

More 8th grade math

Guide for grown-ups