Asolid 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.

10 cones can be made.

Step-by-step 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

288π = n(27π)

n =

n ≈ 10 cones

Therefore, 10 cones can be made.

the answer would be a 24

step-by-step explanation:

c=2πr=2·π·3=24

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²