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INVESTIGATION Purpose: To determine the relationship between the volume of a prism, and the volume of its corresponding pyramid (same base size and height).

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Volume of a Pyramid Archimedes of Syracuse 287 - 212 BC The volume of a pyramid is 1/3 the volume of the surrounding prism on the same base. In the special case, when the pyramid is a cone, the surrounding prism is a cylinder.

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Volume of a Pyramid Example Questions: Find the volume of the pyramids shown. 4 cm 7 cm 8.3 cm 1 Not to SCALE

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4 cm 5 cm 6 cm 3 8 cm 6.1 cm 2 Volume of a Pyramid Questions: Find the volume of the pyramids shown. (1 dp) Not to SCALE 9 cm

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6 cm Example Questions: Find the volume of the cones below. (to 1 dp) 1 2 6.2 cm Not to SCALE 15 cm 4.8 cm

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10 cm Questions: Find the volumes of the cones below. (to 1 dp) 1 2 4.2 m Not to SCALE 19 cm 7.3 m

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Worksheet 1 Volume of a Pyramid Example Questions: Find the volume of the pyramids shown. 4 cm 8.3 cm 1 7 cm 8 cm 9 cm 6.1 cm 2 4 cm 5 cm 6 cm 3 V = Area of Base x Height

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Worksheet 3 1 2 3 4 Volume of a Cone Example Questions: Find the volume of the cones shown.

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Chapter 12 Volume of All 3d figures. Example #1 Height of prism ______ Height of triangle ____ Area of Base ______ Area one rectangle ___ Total SA ________.

Chapter 12 Volume of All 3d figures. Example #1 Height of prism ______ Height of triangle ____ Area of Base ______ Area one rectangle ___ Total SA ________.

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