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# A carpenter constructed a rectangular sandbox with a

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Math Expert
Joined: 02 Sep 2009
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A carpenter constructed a rectangular sandbox with a  [#permalink]

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13 Aug 2012, 07:02
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Difficulty:

5% (low)

Question Stats:

78% (00:50) correct 22% (01:05) wrong based on 1671 sessions

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A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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13 Aug 2012, 07:02
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SOLUTION

A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

Since given that $$volume=L*W*H=10$$, then $$new \ volume=(2L)*(2W)*(2H)=(2*2*2)*(L*W*H)=8*10=80$$.

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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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12 Apr 2013, 09:52
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A quick note on doubling. When you double a length you have 2*L1. When you double all lengths of a rectangle you have (2*L1)(2*L2) = A. An increase of 2^2 or 4. When you double all lengths of a rectangular prism you have (2*L1)(2*L2)(2*L3) = V. An increase of 2^3 or 8.

This leads to the basic relationship:

Line: 2*original size
Rectangle: 4*original size
Rectangular Prism: 8*original size

You can do the math out or memorize this relationship to speed things up.
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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08 Oct 2018, 10:41
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dixxa wrote:
I have a similar question. Why are we not taking the common factor 2(L*B*H)?

Rocket7 wrote:
This may is more of a conceptual question I guess. In 2l *2b*2h can we not take the 2 common such as 2(L*B*H).

L*B*H=10.....-> given.

2L*2B*2H= ?
2(L*B*H)
2(10)=20

Hi dixxa,
Common factors are to be factored out when the terms are either added or substracted in an equation/expression. In case of multiplication or division, it is simply multiplication or division of terms respectively.

Here, in 2L*2B*2H, we have three terms multplied 2L, 2B, and 2H.

From 2L, 2 can be factored out. (you know 2L=2 multiplied by L)

Similarly, From 2B, 2 can be factored out.
Similarly, From 2H, 2 can be factored out.

Now, 2L*2B*2H=2*2*2*L*B*H=8(L*B*H)

Had it been 2L+2B+2H, then we can factor out 2 as '2' is a common factor of 2L, 2B, and 2H, making 2L+2B+2H=2(L+B+H)

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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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13 Aug 2012, 08:16
Let x,y & z be L,W & H
so xyz = 10 cu ft
As per question if we double the lengths on all dimensions
we get (2x)(2y)(2z)=8 xyz= 8*10= 80
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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13 Aug 2012, 08:21
volume =l*b*h =10 cubic feet
Now we have twice as long, twice as wide, and twice as high as the first sandbox,
L=2*l
B=2*b
H=2*h
final volume =L*B*H =2*l*2*b*2*h=8*(l*b*h) =8*10=80 cubic feet

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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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13 Aug 2012, 09:16
V=LWH

Original Volume = 10

In order to keep things simple. I made Height = 5, Length = 2, and Width = 1

The second statement says double everything.

Height = 10, Length = 4, and Width = 2

V = 80
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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02 Dec 2014, 02:30

Original volume = 10 cubic feet

New volume = 10 * 2 * 2 * 2 = 80
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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24 May 2016, 10:43
Bunuel wrote:
A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

We are given a rectangular sandbox with a given capacity, which is the volume of the sandbox.

Therefore, we know that the volume of the sandbox is: (L)(W)(H) = 10 cubic feet

We then are told that the carpenter doubles the length, the width, and the height. We can represent this doubling as (2L)(2W)(2H). Thus

(2L)(2W)(2H) = (2)(2)(2)(L)(W)(H) = (2)(2)(2)(10) = 80 cubic feet

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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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07 Jul 2017, 14:14
Using some simple values, let all sides be equal to 2. The first surface area will be 2*2*2 = 8
Now double all these sides. The new surface area will be 4*4*4=64
64 is 8*8. Hence the answer should be 10*8=80 or D
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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15 Jul 2017, 22:57
I have a small doubt in this question. The volume of a rectangular solid is l*w*h=10*10*10 because the question says its cubic feet. Where am i going wrong in my concept??
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A carpenter constructed a rectangular sandbox with a  [#permalink]

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16 Jul 2017, 03:59
longhaul123 wrote:
I have a small doubt in this question. The volume of a rectangular solid is l*w*h=10*10*10 because the question says its cubic feet. Where am i going wrong in my concept??

We are told that the volume is 10 cubic feet (the volume of 3-D objects is measured in cubic units), not that the lengths of the sides are 10 feet, so it should be l*w*h = 10. Please re-read the solutions above.
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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16 Jul 2017, 04:45
Thank youBunuel.
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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14 Feb 2018, 05:49
This may is more of a conceptual question I guess. In 2l *2b*2h can we not take the 2 common such as 2(L*B*H).

L*B*H=10.....-> given.

2L*2B*2H= ?
2(L*B*H)
2(10)=20
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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08 Oct 2018, 10:05
I have a similar question. Why are we not taking the common factor 2(L*B*H)?

Rocket7 wrote:
This may is more of a conceptual question I guess. In 2l *2b*2h can we not take the 2 common such as 2(L*B*H).

L*B*H=10.....-> given.

2L*2B*2H= ?
2(L*B*H)
2(10)=20
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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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09 Oct 2018, 13:42
Thank you so much for your explanation. It makes sense.

PKN wrote:
dixxa wrote:
I have a similar question. Why are we not taking the common factor 2(L*B*H)?

Rocket7 wrote:
This may is more of a conceptual question I guess. In 2l *2b*2h can we not take the 2 common such as 2(L*B*H).

L*B*H=10.....-> given.

2L*2B*2H= ?
2(L*B*H)
2(10)=20

Hi dixxa,
Common factors are to be factored out when the terms are either added or substracted in an equation/expression. In case of multiplication or division, it is simply multiplication or division of terms respectively.

Here, in 2L*2B*2H, we have three terms multplied 2L, 2B, and 2H.

From 2L, 2 can be factored out. (you know 2L=2 multiplied by L)

Similarly, From 2B, 2 can be factored out.
Similarly, From 2H, 2 can be factored out.

Now, 2L*2B*2H=2*2*2*L*B*H=8(L*B*H)

Had it been 2L+2B+2H, then we can factor out 2 as '2' is a common factor of 2L, 2B, and 2H, making 2L+2B+2H=2(L+B+H)

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Re: A carpenter constructed a rectangular sandbox with a  [#permalink]

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23 Jun 2019, 06:28
Bunuel wrote:
A carpenter constructed a rectangular sandbox with a capacity of 10 cubic feet. If the carpenter were to make a similar sandbox twice as long, twice as wide, and twice as high as the first sandbox, what would be the capacity, in cubic feet, of the second sandbox?

(A) 20
(B) 40
(C) 60
(D) 80
(E) 100

Practice Questions
Question: 18
Page: 154
Difficulty: 550

If each of the sides was increased by a factor of 2,

then the linear ratio is 1:2. In order to get the volume ratio, I need to

cube the linear ratio; so the volume ratio is going to be (1 cubed), to (2 cubed) -- which is 8.

So if this is 10 cubic feet, this is going to be 80 cubic feet, and the correct answer choice is D.
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Re: A carpenter constructed a rectangular sandbox with a   [#permalink] 23 Jun 2019, 06:28
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