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

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2 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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4 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.

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

6 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

7 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

8 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

9 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

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


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