Latest CAT Aptitude Question SOLUTION: a cuboid has a volume of 64cubic units. find the minimum possible values of the sum of the lengths of the edges of the cuboid.

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a cuboid has a volume of 64cubic units. find the minimum possible values of the sum of the lengths of the edges of the cuboid.

Asked In CAT chandani gupta (12 years ago)

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lakshmi reddy  (12 years ago)

lakshmi reddy (3 Min ago)
[lakshmi reddy]
volume of cuboid=l*b*h=64 cubic units
sum of lengths of edges of the cuboid= l+b+h
the minimum possible values of l, b, h are 4, 4 and 4 respectively
l*b*h=4*4*4=64
So, l+b+h=4+4+4=12.....Hence Answer is 12

Is this solution Helpfull? Yes (4) | No   

Utsav Misra  (12 years ago)

answer is 48
explanation:
l*b*h=64 is given
and we have to minimize 4*l+4*b+4*h i.e 4(l+b+h) (since there are 4 lengths , 4 breadths and 4 heights)
so, in order to minimize we can use the A.M >= G.M method meaning by, that arithmetic mean of n numbers is always greater than or equal to their geometric mean....
so, A.M of l,b,h >= G.M of l,b,h
=> (l+b+h)/3 >= (l*b*h)^(1/3) (since G.M is cube root of l*b*h
=> l+b+h >= 12 (since l*b*h=64 which is given)
therefore, 4(l+b+h) >= 48
hence minimum value of the sum of the lengths of the edges of the cuboid is 48.

Is this solution Helpfull? Yes (4) | No   

lakshmi reddy  (12 years ago)

lakshmi reddy (3 Min ago)
[lakshmi reddy]
volume of cuboid=l*b*h=64 cubic units
sum of lengths of edges of the cuboid= l+b+h
the minimum possible values of l, b, h are 4, 4 and 4 respectively
l*b*h=4*4*4=64
So, l+b+h=4+4+4=12.....Hence Answer is 12

Is this solution Helpfull? Yes (1) | No   

lakshmi reddy  (12 years ago)

lakshmi reddy (3 Min ago)
[lakshmi reddy]
volume of cuboid=l*b*h=64 cubic units
sum of lengths of edges of the cuboid= l+b+h
the minimum possible values of l, b, h are 4, 4 and 4 respectively
l*b*h=4*4*4=64
So, l+b+h=4+4+4=12.....Hence Answer is 12

Is this solution Helpfull? Yes (1) | No   

lakshmi reddy  (12 years ago)

lakshmi reddy (3 Min ago)
[lakshmi reddy]
volume of cuboid=l*b*h=64 cubic units
sum of lengths of edges of the cuboid= l+b+h
the minimum possible values of l, b, h are 4, 4 and 4 respectively
l*b*h=4*4*4=64
So, l+b+h=4+4+4=12.....Hence Answer is 12

Is this solution Helpfull? Yes (1) | No   

lakshmi reddy  (12 years ago)

volume of cuboid=l*b*h=64 cubic units
sum of lengths of edges of the cuboid= l+b+h
the minimum possible values of l, b, h are 4, 8 and 2 respectively
l*b*h=4*8*2=64
So, l+b+h=4+8+2=14.....Hence Answer is 14

Is this solution Helpfull? Yes | No (2)  

venkata mounica alapati  (12 years ago)

it has 12 edges. minimum value of edge is 4.
so, the minimum possible values of sum of the length of 12 edges are 12*4=48

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Susmita Das  (9 years ago)

12
because volume of cuboid is = a(cube)
hence a=4.
There are maximum 3 edges.

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