Volume of Pyramids, Cones, and Spheres

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Volume of Pyramids, Cones, and Spheres

• Lesson 8.3B
• M.3.G.2 Apply, using appropriate units,
  appropriate formulas (area, perimeter, surface
  area, volume) to solve application problems
  involving polygons, prisms, pyramids, cones,
  cylinders, spheres as well as composite figures,
  expressing solutions in both exact and
  approximate forms

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Review

• Volume The number of cubic units needed to fill
  a space
• Remember, volume is always measured in units cubed

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Volume of Pyramids

• Volume of a pyramid
• B Area of the Base
• h height of the pyramid (not the slant height)

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Example

• Find the volume of the given pyramid.

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Example 2

• Find the volume of the given pyramid.

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Now You Try

• Find the volume of the given pyramid.

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Volume of Cones

• Volume of a cone V
• r radius of the base
• h height of the cone

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Example

• Find the volume of the cone.

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Now You Try

• Find the volume of the cone.

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Volume of Spheres

• Volume of a sphere
• r radius of the sphere

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Example

• Find the volume of the given sphere.

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Word Problems

• Dixie cups are cones with a 3 inch height and a 2
  inch radius. How much water fits in one Dixie
  cup?

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Example 2

• A spherical ice cream scoop rests on an ice cream
  cone that is shaped like a right cone. Suppose
  the ice cream melts. Will it fit inside the
  cone? Justify your answer. (assume that melted
  and frozen ice cream have equal volume)

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Now You Try

• The top of the Washington Monument in Washington,
  D.C., consists of a regular square pyramid with a
  height of 55 ft. The length of a side of the
  base of the pyramid is about 34.4 ft. Find the
  volume.