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VOLUMES OF CYLINDERS, CONES AND SPHERES

VOLUMES OF CYLINDERS, CONES AND SPHERES. WARM UP. Find the length of a side of a square if the area is 64 cm². Find the length of a cube if the volume is 8 inches². Find the length of a cube if the volume is 125 cm².

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VOLUMES OF CYLINDERS, CONES AND SPHERES

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  1. VOLUMES OFCYLINDERS, CONES AND SPHERES

  2. WARM UP Find the length of a side of a square if the area is 64 cm². Find the length of a cube if the volume is 8 inches². Find the length of a cube if the volume is 125 cm².

  3. Today we are going to prove the relationship between cylinders, cones and spheres. • On your whiteboard, draw a sphere, cylinder and cone. • Can you think of any differences/similarities about the shapes? • Label the base/height of each of the shapes. • What is the shape of the base? • Can you think of a formula we can use to find the volume of a cylinder? • What about a sphere or cone?

  4. On your index card, write the formula for the volume of a cylinder.

  5. Now, let’s perform an experiment to discover how the cone, cylinder and sphere are connected with regards to their volume. Can you predict the volume of each figure? (given that each has the same diameter and height) Let’s look at the relationship between the cone and the sphere first. Prediction: Actual:

  6. On your index card, write the formula for the volume of a cone.

  7. Now, lets look at how the volume of the sphere relates to the cylinder. Can you predict how many times a sphere will fill a cylinder with the same diameter and height? Actual:

  8. Write the formula for the volume of a sphere on your index card.

  9. Let’s try and use our new formulas.

  10. Diameter = 12. Find the volume.

  11. Radius = 8 cm. Find the volume.

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