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A circle with a radius of 4 feet is cut from a piece of sheet metal

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A circle with a radius of 4 feet is cut from a piece of sheet metal  [#permalink]

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New post 21 Aug 2018, 18:29
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Difficulty:

  35% (medium)

Question Stats:

62% (01:30) correct 38% (02:05) wrong based on 34 sessions

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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

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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal  [#permalink]

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New post 21 Aug 2018, 19:09
PeepalTree 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


Weight is calculated from the area.
Given, 20 pounds corresponds to an area of \(\pi(4)^2\)
So area of the circle with unit pound(1 pound)=\(\frac{\pi(4)^2}{20}\)

Since the circle with weight 60 pounds is cut from the same metal sheet we can correlate the unit pounds of the first circle with the second circle.
Hence, area of the circle with 60 pounds=\(\frac{\pi(4)^2}{20}*60\)=\(48\pi\)
So, radius of the circle=\(\sqrt{\frac{48\pi}{\pi}}\)=\(\sqrt{48}\approx{7}\)

Ans. (B)
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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal  [#permalink]

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New post 21 Aug 2018, 22:37

Solution



Given:
    • A circle with a radius of 4 feet is cut from a piece of sheet metal with uniform thickness.
    • The circle weighs 20 pounds.
    • Another circle is cut from the same sheet and weighs 60 pounds.

To find:
    • The radius of the second circle.

Approach and Working:
The weight of the second circle is 3 times the weight of the first circle.
    • Because of uniform thickness, its area will also be 3 times of the area of the first circle.

Now, the area of the first circle = π x 4 x 4 = 16π
    • Hence, the area of the second circle = 3 x 16π = 48π
    • As the area is 48π, the radius should be very close to 7.

Hence, the correct answer is option B.

Answer: B

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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal &nbs [#permalink] 21 Aug 2018, 22:37
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