A circle with a radius of 4 feet is cut

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rsarashi: Master | Next Rank: 500 Posts; Posts: 186; Joined: Sat Dec 24, 2016 12:38 amFollowed by: 3 members; Thanked: 5 times

by rsarashi » Fri Jun 02, 2017 9:12 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

D) 10 feet

OAB

Please explain.

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DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Fri Jun 02, 2017 9:29 am

rsarashi 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

D) 10 feet

OAB

Please explain.

If the second circle is three times the weight of the first (60/20), then it stands to reason that the area of the second circle will be three times the area of the first.

Area of circle with radius 4 = 16 *Pi
Area of second circle that is three times the first = 16Pi * 3 = 48Pi
The radius of a circle with an area 48 * Pi is about 7. (The area of a circle with a radius of 7 is 49Pi.) The answer is B

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by [email protected] » Fri Jun 02, 2017 10:14 am

Hi rsarashi,

This question can be approached in a couple of different ways. Here's how we can solve it by TESTing THE ANSWERS.

We're told that a circle , with a radius of 4 feet, cut from a uniform piece of sheet metal would weigh 20 pounds. Thus, we can equate area with weight...

A = (pi)(R^2) = (pi)(4^2) = 16pi ft^2 = 20 pounds

Thus, every 16pi ft^2 equates to 20 pounds. We're asked to find the approximate radius of a circle that would weight 60 pounds (which is triple the weight of this circle). Thus, we're looking for an area that is approximately triple this area. Let's TEST Answer B...

Answer B: 7 feet

With a radius of 7 feet, this circle would have an area of...
A = (pi)(R^2) = (pi)(7^2) = 49pi = a little more than triple the area of the other circle. While you can TEST Answers A and C if you like, you'll find that Answer B is closest.

Final Answer: B

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Rich

Contact Rich at [email protected]

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by Jay@ManhattanReview » Sat Jun 03, 2017 11:19 pm

rsarashi 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

D) 10 feet

OAB

Please explain.

Weight of a circular disk = Volume of a circular disk * density of metal = Area of the disk * Thickness of the disk * Density of metal

Since the circular disc is cut from the same metal sheet with a uniform piece, Thickness of the disk and Density of metal are constant

Thus, Weight of a circular disk is proportional to Area of the disk

Weight of a circular disk with 4 feet radius / Weight of a circular disk with x feet radius = Area of the disk with 4 feet radius / Area of the disk with x feet radius

=> 20/60 = Ï€*4^2 / Ï€*x^2
=> 1/3 = 16/x^2
=> x = âˆš48 = ~7 feet

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: A circle with a radius of 4 feet is cut

by Scott@TargetTestPrep » Sun Mar 15, 2020 7:50 am

rsarashi wrote: ↑
Fri Jun 02, 2017 9:12 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

D) 10 feet

OAB

Please explain.

The area of the circle of radius 4 feet is 16π. Let r = the radius of the circle that weighs 60 pounds. Thus, the area of such a circle is πr^2. Since the weight of the circle is proportional to its area, we have:

16π / 20 = πr^2 / 60

Multiplying the equation by 60, we obtain:

48π = πr^2

r^2 = 48

r ≈ 7

Answer: B

Scott Woodbury-Stewart
Founder and CEO
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