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# A 10-by-6 inch piece of paper is used to form the lateral

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A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  28 Jul 2011, 08:34
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A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
[Reveal] Spoiler: OA
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baker2145 wrote:
Here's the question:

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

I am having difficulty with this one: Please help and explain, if answer if B or E, WHY it is (#/pi) and not #pi, considering pi(r-squared)(h) is the volume formula

Thanks,

6 or 10 will be circumference ...so 2 * pi* r = 6 or 10 and hence r = #/pi....and difference would be 60/pi [applying the volume formula and taking the difference] ...would go with B
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when the paper is folded with the 10 as the height .. 6 will be the circumference not the radius.. so 2*pi*r = 6 -> r = 3/ pi.. then its pretty straightforward.. pi ( r1*r1*h1 - r2*r2*h)
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baker2145 wrote:
Here's the question:

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

I am having difficulty with this one: Please help and explain, if answer if B or E, WHY it is (#/pi) and not #pi, considering pi(r-squared)(h) is the volume formula

Thanks,

Hopefully, you have some intuition about which of the possible cylinders is going to have the greater volume. Because the volume of a cylinder is directly proportional to the height and directly proportional to the square of the radius, the size of the radius has the greatest effect on the volume of the cylinder. Given this intuition we can eliminate A and C.

The answer given already is correct, but I'm going to provide some more details in term of calculation

Cylinder with height 10 and circumference 6:
$$2pi(r) = 6$$
$$r = \frac{3}{(pi)}$$
$$V = (pi)(\frac{3}{pi})^2(10)$$
$$V = \frac{90}{pi}$$

Cylinder with height 6 and circumference 10:
$$2pi(r) = 10$$
$$r = \frac{5}{(pi)}$$
$$V = (pi)(\frac{5}{pi})^2(6)$$
$$V = \frac{150}{pi}$$

150-90 = 60

So, B.
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Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 6 and 10 are the circumference of the base and not the radius. B is the right answer.
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A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  28 Feb 2013, 10:40
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

(A)The volume of the cylinder with height 10 is 60 / cubic inches greater than the volume of the cylinder with height 6.

(B)The volume of the cylinder with height 6 is 60 / cubic inches greater than the volume of the cylinder with height 10.

(C)The volume of the cylinder with height 10 is 60 cubic inches greater than the volume of the cylinder with height 6.

(D)The volume of the cylinder with height 6 is 60 cubic inches greater than the volume of the cylinder with height 10.

(E)The volume of the cylinder with height 6 is 240 / cubic inches greater than the volume of the cylinder with height 10.
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Re: A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  28 Feb 2013, 12:24
mun23 wrote:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

(A)The volume of the cylinder with height 10 is 60 / cubic inches greater than the volume of the cylinder with height 6.

(B)The volume of the cylinder with height 6 is 60 / cubic inches greater than the volume of the cylinder with height 10.

(C)The volume of the cylinder with height 10 is 60 cubic inches greater than the volume of the cylinder with height 6.

(D)The volume of the cylinder with height 6 is 60 cubic inches greater than the volume of the cylinder with height 10.

(E)The volume of the cylinder with height 6 is 240 / cubic inches greater than the volume of the cylinder with height 10.

Radius of 1 cylinder 6*10 (l*h) is 2pi r1 = 6
Radius of 2 cylinder 10*6 (l*h) is 2pi r2 = 10

Volume of cylinder is pi r square * h

Volume of 1 cylinder = 90/pi
volume of 2 = 150/pi
Difference = 60/pi
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Re: A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  03 Mar 2013, 07:19
The answer B should have a pi included in it bacuase it is actual amout is 18 cubic inches difference but / pi
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Re: A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  03 Mar 2013, 13:06
This isn't really a 700 Question, is it ?
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Re: A 10-by-6 inch piece of paper is used to form the lateral [#permalink]  15 Aug 2014, 05:37
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Re: A 10-by-6 inch piece of paper is used to form the lateral   [#permalink] 15 Aug 2014, 05:37
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