A solid metal sculpture in Kamila’s backyard is in the shape of a sphere and has a radius of 6 inches. She wants to have it melted and made into small solid cones. She would like the cones to each have a diameter of 6 inches and a height of 9 inches. With these dimensions, how many cones can be made from the metal sphere?In your final answer, include all formulas, equations, and calculations necessary to determine how many cones can be made.
Accepted Solution
A:
Volume of sphere is 4πr³/3 and volume of cone is ⅓πr²h, where r is radius and h is cone height. Vol of Kamila’s sphere 4π(216)/3=288π Vol of cone=π(9)(9)/3=27π Total number of cones is 288/27=32/3=10 complete cones.