Question

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.

Answer 1

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.

Answer 2

10 cones can be made.

Explanation:

A solid metal sculpture in Kamila's backyard is in the shape of a sphere with a radius of 6 inches.

She melts this sphere to make small solid cones with diameter of 6 inches and height of 9 inches.

In this process Total volume of the metal will remain same.

Volume of sphere = Number of cones × Volumes of one cone

`(4)/(3)\pi r^(3)=n[((1)/(3))\pi r^(2)h]`

`(4)/(3)\pi 6^(3)=n[((1)/(3))\pi (3^(2))(9)]`

`(4)/(3)\pi (216)=n[((1)/(3))\pi (9)(9)]`

288π = n(27π)

n =
`(288\pi )/(27\pi )= 10.67`

n ≈ 10 cones

Therefore, 10 cones can be made.