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Volume of Pyramids and Cones

Volume of Pyramids and Cones. “If I had influence with the good fairy… I should ask that her gift to each child in the world be a sense of wonder so indestructible that it would last throughout life.” Rachel Carson. Objectives. Discover formulas for the volumes of pyramids and cones.

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Volume of Pyramids and Cones

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  1. Volume of Pyramids and Cones “If I had influence with the good fairy… I should ask that her gift to each child in the world be a sense of wonder so indestructible that it would last throughout life.” Rachel Carson

  2. Objectives • Discover formulas for the volumes of pyramids and cones. • Practice three-dimensional visual thinking skills.

  3. Pyramids and Cones What do all these shapes have in common?

  4. Investigation The Volume Formulas for Pyramids and Cones p 522 Pyramid-Cone Volume Conjecture If B is the area of the base of a pyramid or a cone and H is the height of the solid, then the formula for the volume is V = ___________. BH

  5. Example The shape to the left is a regular pentagonal pyramid. Find the volume of the shape. Height = 8cm 6 cm

  6. Solution We must find the length of the apothem B = ½ * a *p B = ½ * 3 (3)*(6)(5) B = ½ * 3 (3)*30 B = 15* 3 (3) B = 45 (3) 6cm V = * B * H 3cm 3cm V = * 45 (3) * 8 Apothem = 3(3) V = 120(3)cm3

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