Problema Solution
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 provided by our tutors
the volume of the solid sphere with radius of 6 in is:
V = (4/3)6^3pi
V = 288 pi in^3
the volume of small solid code is:
V1 = (1/3)(6/2)^2 pi *9
V1 = 27 pi in^3
let 'n' represent the number of cones, n is integer
nV1 <= V
n*27pi <= 288 pi divide both sides by pi
27n <= 288
n <= 10.66
click here to see the step by step solution of the inequality:
there can be 10 cones made at most.