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The dimensions of a field are 20 m by 9 m. A pit 10 m long,

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005ashok
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The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   Updated on: 19 Jan 2014, 23:21
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The dimensions of a field are 20 m by 9 m. A pit 10 m long, 4.5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?

A. 15 m
B. 2 m
C. 3 m
D. 4 m
E. 1 m
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E

Originally posted by 005ashok on 19 Jan 2014, 21:35.
Last edited by Bunuel on 19 Jan 2014, 23:21, edited 1 time in total.
Edited the question and added the OA.
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Bunuel
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   19 Jan 2014, 23:26
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005ashok wrote:
The dimensions of a field are 20 m by 9 m. A pit 10 m long, 4.5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?

A. 15 m
B. 2 m
C. 3 m
D. 4 m
E. 1 m


The volume of the earth removed is 10*4.5*3 = 135 m^3.

The remaining area of the field is 20*9 - 10*4.5 = 135 m^2.

135 m^3 of the earth evenly spread over the area of 135 m^2 will rise the height by (height) = (volume)/(area) = 135/135 = 1 m.

Answer: E.

Hope it's clear.
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   20 Jan 2014, 01:38
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005ashok wrote:
The dimensions of a field are 20 m by 9 m. A pit 10 m long, 4.5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?

A. 15 m
B. 2 m
C. 3 m
D. 4 m
E. 1 m


this is pretty simple but avoid making mistakes during calculations

the vol of soil ploughed = vol of soil spread on the remaining ground

10*4.5*3=(10*9+10*4.5)*x
=> x=1
to understand the above equation, draw a figure yourself
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   16 Jul 2017, 18:20
tricky question, as it talks about volume and surface area...so it might be confusing at first...
I solved the question the way Bunuel explained. we get 1M.
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   18 Jul 2017, 03:45
Option E
10*4.5*3=h*(10*4.5+20*4.5)
h=1 m
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   07 May 2018, 13:07
005ashok wrote:
The dimensions of a field are 20 m by 9 m. A pit 10 m long, 4.5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field. What will be the rise in the height of field as a result of this operation ?

A. 15 m
B. 2 m
C. 3 m
D. 4 m
E. 1 m


The volume is 10*4.5*3 = 135

The remaining area is 20*9 - 10*4.5 = 135 m^2.

rise in the height = (volume)/(area) = 135/135 = 1 m.
E
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   23 May 2018, 08:15
The volume of the earth removed is 10*4.5*3 = 135.

The remaining area of the field (do not consider height here,only consider area) is (20*9) - (10*4.5) = 135

So height =135/135=1m

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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   14 Aug 2021, 10:29
Let the rise in the height of field be h.

Volume of earth removed = Volume of Earth spread
\(10 m * 4.5 m * 3 m = (20 * 9 - 10 * 4.5)m^2 * h\)
\(h = \frac{135}{135} m = 1 m\)

Hence, OA is (E).
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink] New post   14 Aug 2021, 20:15
L W D
Field 20 9 - \( F area = 20*9 = 180 m^2\)
Pit 10 4.5 3 \( P area=10*4.5=45 m^2 P Volume=10*4.5*3=135 m^3\)
Ramming area = \(area 1-area 2 \) (Avoid mistake! Area- Area NOT \( (L1-L2)* (W1- W2) \))
\(=180-45 m^2\)
\( =135 m^2\)

Now,\(\frac{ Volume}{Area}=Depth \)

\( = \frac{135 m^3}{135 m^2 }=\frac{1 m^1}{1} = 1m\)
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Re: The dimensions of a field are 20 m by 9 m. A pit 10 m long, [#permalink]
14 Aug 2021, 20:15
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