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.

Question

Mathematics

Willow Lutz

20 February, 07:40

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.

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Answers (1)

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Mathew Fleming · Answer 1

Assuming that the process of transforming the sphere into cones there would be no losses

V_sphere = n (V_cones)

V_sphere = (4/3) (PI) (r^3)

= 904.7787 in3

V_cones = (1/3) (PI) (R^2) (H)

= 84.8230 in3

n = (V_sphere) / (V_cones)

= (904.7787) / (84.8280)

= 10.667

~ 10 cones