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

Question

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

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

Bunuel · Accepted Answer

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.

bharatdivvela · Answer

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

mvictor · Answer

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.

tapasgupta · Answer

Option E
10*4.5*3=h*(10*4.5+20*4.5)
h=1 m

devikeerthansr · Answer

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

push12345 · Answer

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

Posted from my mobile device

v12345 · Answer

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).

SalahT · Answer

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

luisdicampo · Answer

Deconstructing the Question

Topic: Volume and Surface Area

The core principle here is that the  Volume of earth removed  is equal to the  Volume of earth spread  over the remaining area.

1. Calculate Volume of Earth Removed  
The pit is a rectangular prism:
 Volume = length * width * depth 
 Volume = 10 * 4.5 * 3 =    135 m3

2. Calculate the Remaining Area  
The earth is spread only over the area  not  occupied by the pit:
 
 Total Field Area =  20 * 9 = 180 m2  
 Area of the Pit =  10 * 4.5 = 45 m2  
 Remaining Area =  180 - 45 =    135 m2

3. Find the Rise in Height (h)  
 Volume spread = Area * Rise 
 135 m3 = 135 m2 * h 
 h =    1 m

The correct answer is E.

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

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

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