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Understanding Cylinder and Cone Volumes: Formulas and Differences

Discover the formulas for cylinder and cone volumes, their similarities, and differences. Learn how to calculate the volume of a cylinder and cone using base area and height measurements. Find out the key variances in volumes between cylinders and cones with the same bases and heights.

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Understanding Cylinder and Cone Volumes: Formulas and Differences

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  1. 9-2C Volume of Cylinders and Cones What is the difference in volume between cylinders and cones with the same area bases and same height? How do you find the formula for the volume of a cylinder? How do you find the formula for the volume of a cone?

  2. Similarities and Differences… • Pyramid is to prism as _______ is to cylinder. • Prism is to cylinder as pyramid is to______. cone cone ?

  3. Volume of a Cylinder The volume of a cylinder is the product of its base area and its height. V = π r2 H r r H H

  4. Find the Volume… V = π r2 H V = π (12.3)2(22.1) V = 3343.509 π (exact) V = 10,503.9 (approx) 12.3 22.1

  5. Water Test • How many cones will it take to fill a cylinder? • How do you find the formula for volume of a cone? • What is the shape of the base? • Go to cone • Go to volume formula

  6. Volume of a Cone The volume of a cone is one-third the product of its base area and its height. V = ⅓ π r 2 H H r

  7. Find the Volume… V = ⅓ π r 2 H V = ⅓ π (4.3)2(6.7) V = 41.29π (exact) V = 129.73 (approx) 6.7 4.3

  8. What is the difference in volume between cylinders and cones with the same area bases and same height? ⅓ • How do you find the formula for the volume of a cylinder? A cone? What is the shape of the base? Circle Find circle Find cylinder or cone Find Volume formula

  9. Assignment9-2C Page 637, 1-9, 26-29 No formulas with numbers, NO CREDIT

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