GreenlightTestPrep wrote:
If a solid metal cylinder with radius 3 and height 12 is melted and then formed into a solid sphere, what is the radius of the sphere?
Note: Volume of sphere = (4/3)(π)(radius³)
A) ∛6
B) ∛12
C) ∛36
D) 3
E) 3∛3
Key concept:
the volume of the cylinder =
the volume of the spherevolume of the cylinder = πr²h
= π(3²)(12)
= 108πSo,
the volume of the sphere = 108πVolume of sphere = (4/3)(π)(radius³)
So,
(4/3)(π)(radius³) = 108πDivide both sides by π to get: (4/3)(radius³) = 108
Multiply both sides by 3 to get: (4)(radius³) = 324
Divide both sides by 4 to get: radius³ = 81
So, radius = ∛81
Check the answer choices....not there! Looks like we need to simplify ∛81
Notice that 81 = 27 x 3
So, ∛81 = ∛27 x ∛3
= 3 x ∛3
= 3∛3
Answer: E
Cheers,
Brent