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A carpenter constructed a rectangular sandbox with a [#permalink]
13 Aug 2012, 06:02
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Difficulty:
5% (low)
Question Stats:
78% (01:38) correct
22% (00:45) wrong based on 662 sessions
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
Re: A carpenter constructed a rectangular sandbox with a [#permalink]
13 Aug 2012, 06:02
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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 \(new \ volume=(2L)*(2W)*(2H)=(2*2*2)*(L*W*H)=8*10=80\).
Re: A carpenter constructed a rectangular sandbox with a [#permalink]
13 Aug 2012, 07:16
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 Answer: D _________________
Re: A carpenter constructed a rectangular sandbox with a [#permalink]
13 Aug 2012, 07:21
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
Re: A carpenter constructed a rectangular sandbox with a [#permalink]
17 Aug 2012, 00:02
Expert's post
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 \(new \ volume=(2L)*(2W)*(2H)=(2*2*2)*(L*W*H)=8*10=80\).
Re: A carpenter constructed a rectangular sandbox with a [#permalink]
12 Apr 2013, 08:52
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.
Re: A carpenter constructed a rectangular sandbox with a [#permalink]
01 Dec 2014, 15:17
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