Volume of Cones

Focus 12 - Learning Goal: The student will know and use the formulas for volume of cones, cylinders and spheres. 4 3 2 1 In addition to 3, student will be able to go above and beyond by applying what they know about volume of cones, spheres and cylinders.   The student will know and use the formulas for volume of cones, cylinders and spheres. - Students can apply these formulas to solve real-world mathematical problems. With no help the student has a partial understanding of volume of cones, cylinders and spheres. With help, the student may have a partial understanding of volume of cones, cylinders and spheres. Even with help, the student is unable to find the volume of cones, cylinders and spheres.

Cone V = 1/3 (π r2 h) To calculate the volume of a cone. 1. Square the radius Multiply by height Divide by 3 (which is the same as multiplying by 1/3) Leave answers in terms of π.

Find the volume of the cone. V = 1/3 (π r2 h) V = 1/3 (π) (42) (6) V = 1/3 (π) (16) (6) V = 1/3 (π) (96) V = 32 π inches3

Find the volume of the cone. V = 1/3 (π r2 h) V = 1/3 (π) (52) (10) V = 1/3 (π) (25) (10) V = 1/3 (π) (250) V = 831/3 π m3

Work the problem backwards: The volume of a cone is 196π ft3. The radius is 7 ft. What is the height of the cone? Since we are missing the height, work the problem backward. V = 1/3 (π r2 h) 196π = 1/3(π • 72)h 588π = (49π)h 49 π 49π 12 = h Multiply both sides by the reciprocal of 1/3. This would be 3. The height of the cone is 12 ft.