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Carpenter

by MBA.Aspirant » Mon Nov 21, 2011 3:50 am
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

I think there's a rule regarding similar shapes, for example if the length is doubled, then area is 4 times the original area. is it the same for volume, but the volume is 8 times?
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by pankajks2010 » Mon Nov 21, 2011 4:03 am
Hi, Although, I am not aware of any formula on this concept. However, I think the rule that you are speaking about would be applicable in the case of a cube (for volume)/ square (for area).

For this question, the figure would be a cuboid. So, lbh (volume) = 10
Now, 2l*2b*2h=8lbh=8*10=80. Thus, (D)
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by GMATGuruNY » Mon Nov 21, 2011 4:04 am
MBA.Aspirant 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

I think there's a rule regarding similar shapes, for example if the length is doubled, then area is 4 times the original area. is it the same for volume, but the volume is 8 times?
Let l = 1, w = 1, and h = 10, so that V = lwh = 1*1*10 = 10.
When all three dimensions are doubled, new l = 2, new w = 2, new h = 20.
New V = 2*2*20 = 80.

The correct answer is D.

If all of the dimensions of a rectangular solid are increased by a factor of x, then the volume will increase by a factor of x³:
(x*l)(x*w)(x*h) = x³(lwh).
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by neelgandham » Mon Nov 21, 2011 4:47 am
MBA.Aspirant wrote:I think there's a rule regarding similar shapes, for example if the length is doubled, then area is 4 times the original area. is it the same for volume, but the volume is 8 times?
I would recommend you to make use of the formula instead of making use of the rules as rules tend to confuse us at times. The answer to the question is definitely 80 and the solution is provided above by Mitch and Pankaj but here is an example where you will appreciate the use of formulae.

A carpenter constructed a cylinder(1) with a total surface area of 10 square feet. If the carpenter were to make a similar cylinder(2) with twice the height and same radius (as cylinder(1)) then the ratio of area of cylinder(1) to the ratio of area of cylinder(2) is ?

a) 1:2
b) 1:4
c) 1:8
d) 1:1
e) Cannot be determined.

I know the above question is horribly framed but if you answer the question you will really appreciate the idea of using formulae.
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by Jeff@TargetTestPrep » Tue Apr 14, 2015 3:31 am
MBA.Aspirant 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

I think there's a rule regarding similar shapes, for example if the length is doubled, then area is 4 times the original area. is it the same for volume, but the volume is 8 times?
Solution:

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

The Answer is D

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