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

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LordStark
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A circle with a radius of 4 feet is cut from a piece of sheet metal [#permalink] New post  21 Aug 2018, 19:29
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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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PKN
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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal [#permalink] New post  21 Aug 2018, 20:09
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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] New post  21 Aug 2018, 23:37
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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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ScottTargetTestPrep
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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal [#permalink] New post  17 Mar 2020, 10:00
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LordStark 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


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
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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal [#permalink] New post  23 Jun 2021, 09:49
ScottTargetTestPrep why is the weight calculated from the area and not circumference. If circumference is used, the new circle will have a circumference of \(24pi\).

ScottTargetTestPrep wrote:
LordStark 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


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
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adityasuresh
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Re: A circle with a radius of 4 feet is cut from a piece of sheet metal [#permalink] New post  10 Mar 2023, 20:23
Since the question mentions closest to: we can approximate, we can take pie=3
So area of sheet(circular) with radius = 4 = pie *r^2 so 3*4*4 =48 this weighs 20 pounds
When another sheet(circular) is cut it weights 60 pounds
We can use variation, to find the square feet in area of the circle cut. 60/20*48 =144
144 = pie*r^2
144 =3r^2
~49 =r^2
7 = r
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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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