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Lesson Plans and Worksheets for Geometry

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More Lessons for Geometry

Common Core For Geometry

Student Outcomes

- Students give an informal argument using Cavalieriβs principle for the volume formula of a sphere and use the volume formula to derive a formula for the surface area of a sphere.

**The Volume Formula of a Sphere**

Classwork

**Opening Exercise**

Picture a marble and a beach ball. Which one would you describe as a sphere? What differences between the two could possibly impact how we describe what a sphere is?

**Example**

Use your knowledge about the volumes of cones and cylinders to find a volume for a solid hemisphere of radius R.

**Exercises**

- Find the volume of a sphere with a diameter of 12 cm to one decimal place.
- An ice cream cone is 11 cm deep and 5 cm across the opening of the cone. Two hemisphere-shaped scoops of ice cream, which also have diameters of 5 cm, are placed on top of the cone. If the ice cream were to melt into the cone, would it overflow?
- Bouncy rubber balls are composed of a hollow rubber shell 0.4" thick and an outside diameter of 1.2". The price of
the rubber needed to produce this toy is $0.035/in
^{3}. a. What is the cost of producing 1 case, which holds 50 such balls? Round to the nearest cent. b. If each ball is sold for $0.10, how much profit is earned on each ball sold?

**Lesson Summary**

**SPHERE**: Given a point πΆ in the three-dimensional space and a number π > 0, the sphere with center πΆ and radius π
is the set of all points in space that are distance π from the point πΆ.

**SOLID SPHERE OR BALL**: Given a point πΆ in the three-dimensional space and a number π > 0, the solid sphere (or ball)
with center πΆ and radius π is the set of all points in space whose distance from the point πΆ is less than or equal to π.

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