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A carpenter constructed a rectangular sandbox with a [#permalink]
13 Aug 2012, 06:02

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73% (01:34) correct
27% (00:41) wrong based on 324 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

1

This post received KUDOS

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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.