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LordStark
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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ScottTargetTestPrep why is the weight calculated from the area and not circumference. If circumference is used, the new circle will have a circumference of \(24pi\).

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LordStark
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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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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