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If a solid metal cylinder with radius 3 and height 12 is mel

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by Brent@GMATPrepNow » Mon Jul 23, 2018 1:28 pm

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E

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Difficulty—

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

Answer: E
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

*I'll post a solution in 2 days
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Source: — Problem Solving |

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by Brent@GMATPrepNow » Wed Jul 25, 2018 6:17 am
Brent@GMATPrepNow 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

Answer: E
Difficulty level: 600 - 650
Source: www.gmatprepnow.com

*I'll post a solution in 2 days
Key concept: the volume of the cylinder = the volume of the sphere

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

So, the volume of the sphere = 108Ï€
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
Brent Hanneson - Creator of GMATPrepNow.com
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by swerve » Wed Jul 25, 2018 9:26 am
The new sphere will have the same volume of Cylinder.

So, the volume of the sphere = volume of the cylinder

(4/3)(Ï€)(R^3) = (Ï€)(r^2)(h), where R is the radius of the sphere and r is the radius of the cylinder.

Solving for R in the above formula gives the answer E. Regards!
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