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Developing the Formula for the Volume of a Sphere

Developing the Formula for the Volume of a Sphere. OR. =. +. Volume of a Sphere. Using relational solids and pouring material we noted that the volume of a cone is the same as the volume of a hemisphere (with corresponding dimensions)

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Developing the Formula for the Volume of a Sphere

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  1. Developing the Formula for the Volume of a Sphere

  2. OR = + Volume of a Sphere Using relational solids and pouring material we noted that the volume of a cone is the same as the volume of a hemisphere (with corresponding dimensions) Using “math language” Volume (cone) = ½ Volume (sphere) Therefore 2(Volume (cone)) = Volume (sphere)

  3. OR = ÷ 3 Volume of a Sphere We already know the formula for the volume of a cone.

  4. Height BASE Volume of a Sphere AND we know the formula for the volume of a cylinder

  5. = ÷ 3 2 X = Volume of a Sphere SUMMARIZING: Volume (cylinder)= (Area Base) (height) Volume (cone)= Volume (cylinder)/3 Volume (cone)= (Area Base) (height)/3 AND2(Volume (cone)) = Volume (sphere)

  6. 2 X = r h r Volume of a Sphere 2(Volume (cone)) = Volume (sphere) 2( ) (height)/3= Volume (sphere) 2()(h)/3= Volume (sphere) BUT h = 2r 2(r2)(2r)/3 = Volume(sphere) 4(r3)/3 = Volume(sphere) Area of Base r2

  7. Volume of a Sphere

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