Circles

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jain2016: Master | Next Rank: 500 Posts; Posts: 313; Joined: Tue Oct 13, 2015 7:01 am; Thanked: 2 times

by jain2016 » Sun Apr 03, 2016 3:47 am

A circle with a radius of 4 feet is cut from a piece of sheet metal with uniform thickness. The circle weighs 20 pounds. If another circle is cut from the same sheet and weighs 60 pounds, then its radius is closest to which of the following?

A) 6 feet

B) 7 feet

C) 8 feet

D) 9 feet

E) 10 feet

OAB

Hi Experts ,

Please explain.

Thanks,

SJ

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Source: Beat The GMAT — Problem Solving | Sun Apr 03, 2016 3:47 am

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Sun Apr 03, 2016 5:09 am

jain2016 wrote:A circle with a radius of 4 feet is cut from a piece of sheet metal with uniform thickness. The circle weighs 20 pounds. If another circle is cut from the same sheet and weighs 60 pounds, then its radius is closest to which of the following?

A) 6 feet

B) 7 feet

C) 8 feet

D) 9 feet

E) 10 feet

OAB

Hi Experts ,

Please explain.

Thanks,

SJ

Ratio of Volumes = ratio of weights

if h is the thinkness and r is the radius of new circle the,

Pi 4^2*h / Pi r^2*h = 20/60

i.e. r^2 = 16*(3) = 48

i.e. r = 7 approximately

Answer: option B

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by [email protected] » Sun Apr 03, 2016 9:10 am

Hi jain2016,

The amount of work that you need to do so answer this question will depend a bit on how quickly you see the patterns involved.

Since the circle with a radius of 4 weights 20 pounds, we know that...

pi(R^2) = pi(4^2) = 16pi --> 20 pounds

We're then asked to figure out the radius of a circle that weights 60 pounds. Since 60 = 3(20), we need an area that equals 3(16pi) = 48pi. If you have your 'perfect squares' memorized, then you know that 7^2 = 49, so the radius of that larger circle is really close to 7.

Final Answer: B

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