# 8. Find the volume of spheres (FP)

teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Content.8.G.C.9 http://corestandards.org/Math/Content/8/G/C/9
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2

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Lesson objective: Fluently calculate both the exact and approximate volumes of spheres.

This lesson helps to build fluency with calculating the volume of a sphere by illustrating its relationship to the volume of a cylinder. A sphere inscribed within a cylinder is used here because it highlights the relationship between the diameter of the sphere and the height of the cylinder. This work develops students' understanding that the volume of a sphere is $$\frac23$$ of the volume of a cylinder.

Students engage in Mathematical Practice 1 (make sense of problems and persevere in solving them) as they identify and use the dimensions of spheres to find their volumes.

Key vocabulary:

• area
• base
• cylinder
• diameter
• hemisphere
• sphere
• volume
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