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80 pie square inches of material of negligible thickness are required

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80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 12 Jun 2019, 23:59
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80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?

A. \(2\pi\)

B. \(11\pi\)

C. \(178\pi\)

D. \(711\pi\)

E. \(1280\pi\)

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80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 18 Jun 2019, 21:31
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Hungluu92vn azoz7 Aim015 ayush19 stne
Here is how i solved it:
Original barrel diameter = 160 inches, hence radius = 80 inches
Now we are told scaled model is 1/16 times original. Hence the radius of scale model is 80/16 = 5 inches.
Now surface area = 2(pi)r*h + 2*pi*r^2 = 80*pi
substitute r = 5 in above formula we get h = 3 inches.
Now this is the height of the model.
So height of original barrel is 3*16 = 48 inches.

Now we know height and radius of original barrel. so we can convert into feet, since final answer is required in feet.
Height = 48 inches = 4 feet
Radius = 80 inches = 20/3 feet.

Now volume of barrel = pi*r^2*h = pi*(20/3)^2*4 = (1600/9)*pi = ~178*pi
Hence answer is D

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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 13 Jun 2019, 02:23
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Bunuel wrote:
80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?

A. \(2\pi\)

B. \(11\pi\)

C. \(178\pi\)

D. \(711\pi\)

E. \(1280\pi\)


2*pi*r*(h+r)= 80*pi*16*16
solve for h = 48 inches = 4 feet
and radius = 80 inches ; 20/3 feet
so vol ; pi * r^2*h = pi*20*20/9 * 4 = 178 pi
IMO C
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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 14 Jun 2019, 04:52
Archit3110 wrote:
Bunuel wrote:
80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?

A. \(2\pi\)

B. \(11\pi\)

C. \(178\pi\)

D. \(711\pi\)

E. \(1280\pi\)


2*pi*r*(h+r)= 80*pi*16*16
solve for h = 48 inches = 4 feet
and radius = 80 inches ; 20/3 feet
so vol ; pi * r^2*h = pi*20*20/9 * 4 = 178 pi
IMO C


Hi, How come you have multiplied 2 16s in your first line ?? Could you please explain that part?
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80 pie square inches of material of negligible thickness are required  [#permalink]

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New post Updated on: 16 Jun 2019, 01:17
Archit3110 wrote:
Bunuel wrote:
80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?

A. \(2\pi\)

B. \(11\pi\)

C. \(178\pi\)

D. \(711\pi\)

E. \(1280\pi\)


2*pi*r*(h+r)= 80*pi*16*16
solve for h = 48 inches = 4 feet
and radius = 80 inches ; 20/3 feet
so vol ; pi * r^2*h = pi*20*20/9 * 4 = 178 pi
IMO C


Can anyone else explain this in a better manner, sorry, this solution is not making sense to me.
Why are we multiplying by 16 twice ?
The total surface area is \(2\pi r*h +2\pi r^2\) this is equal to \(80\pi\), right? And this is 1/16 of the actual thing or what ????
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Originally posted by stne on 15 Jun 2019, 00:55.
Last edited by stne on 16 Jun 2019, 01:17, edited 1 time in total.
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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 15 Jun 2019, 08:32
Bunuel wrote:
80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?

A. \(2\pi\)

B. \(11\pi\)

C. \(178\pi\)

D. \(711\pi\)

E. \(1280\pi\)


Hi Bunuel, Could you please explain the solution of this problem?
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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 15 Jun 2019, 11:03
ayush19 wrote:
Archit3110 wrote:
Bunuel wrote:
80 pie square inches of material of negligible thickness are required to construct a 1/16 scale model of a cylindrical barrel. If the diameter of the base of the barrel is 160 inches, then what is the volume of the barrel, to the nearest cubic foot?

A. \(2\pi\)

B. \(11\pi\)

C. \(178\pi\)

D. \(711\pi\)

E. \(1280\pi\)


2*pi*r*(h+r)= 80*pi*16*16
solve for h = 48 inches = 4 feet
and radius = 80 inches ; 20/3 feet
so vol ; pi * r^2*h = pi*20*20/9 * 4 = 178 pi
IMO C


Hi, How come you have multiplied 2 16s in your first line ?? Could you please explain that part?
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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 15 Jun 2019, 21:44
Interesting question. I always struggle with questions that use difficult language.
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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 16 Jun 2019, 00:56
BM and waiting for the answer
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Re: 80 pie square inches of material of negligible thickness are required  [#permalink]

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New post 20 Jun 2019, 07:39
ruchik wrote:
Hungluu92vn azoz7 Aim015 ayush19 stne
Here is how i solved it:
Original barrel diameter = 160 inches, hence radius = 80 inches
Now we are told scaled model is 1/16 times original. Hence the radius of scale model is 80/16 = 5 inches.
Now surface area = 2(pi)r*h + 2*pi*r^2 = 80*pi
substitute r = 5 in above formula we get h = 3 inches.
Now this is the height of the model.
So height of original barrel is 3*16 = 48 inches.

Now we know height and radius of original barrel. so we can convert into feet, since final answer is required in feet.
Height = 48 inches = 4 feet
Radius = 80 inches = 20/3 feet.

Now volume of barrel = pi*r^2*h = pi*(20/3)^2*4 = (1600/9)*pi = ~178*pi
Hence answer is D

Please give kudos if you like the explanation.



Thanks ruchik for the explanation.
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Re: 80 pie square inches of material of negligible thickness are required   [#permalink] 20 Jun 2019, 07:39
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