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If a solid metal cylinder with radius 3 and height 12

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If a solid metal cylinder with radius 3 and height 12 [#permalink] New post 23 Jul 2018, 13:38
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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
[Reveal] Spoiler: OA

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Re: If a solid metal cylinder with radius 3 and height 12 [#permalink] New post 24 Jul 2018, 00:00
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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


Volume of cylinder = \(\pi * {Radius}^2 * Height = \pi * 3^2 * 12 = 108\pi\)

Now Volume of cylinder = Volume of sphere (Since the cylinder is melted to made sphere)

or \(108\pi = 4/3 * \pi * {Radius}^3\)

or \({Radius}^3 = 81\)

or Radius of Sphere = \(3∛3\)
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Re: If a solid metal cylinder with radius 3 and height 12 [#permalink] New post 25 Jul 2018, 06:25
Expert's post
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 sphere

volume of the cylinder = πr²h
= π(3²)(12)
= 108π


So, the volume of the sphere = 108π
Volume of sphere = (4/3)(π)(radius³)
So, (4/3)(π)(radius³) = 108π
Divide 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
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Re: If a solid metal cylinder with radius 3 and height 12   [#permalink] 25 Jul 2018, 06:25
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