Latest Elitmus Aptitude Question SOLUTION: What is the volume of biggest cone that can be fit in a cuboid of height 12*10*15?

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What is the volume of biggest cone that can be fit in a cuboid of height 12*10*15?

Asked In Elitmus shikha singh (9 years ago)

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pradeep kumar  (9 years ago)

ans:- 125pi

Is this solution Helpfull? Yes (6) | No (8)  

Kanhaiya Kumar  (9 years ago)

If we take choose the 12*15 face of cuboid for the base of cone then clearly the radius of the right circular is 6 and height is 10.
Hence volume of the cone is= 1⁄3 πr^2h = 120h

Is this solution Helpfull? Yes (3) | No (2)  

veer kumar  (9 years ago)

3 cases are possible of base
1.(12,10)=>diameter=10 and height=15 volume=(1/3)*pi*5^2*15=125pi
2.(10,15)=>""""""""=10 """"""""""=12 volume=(1/3)*pi*5^2*12=100pi
3.(12,15)=>""""""""=12 """"""""""=10 volume=(1/3)*pi*6^2*10=120pi
clearly the biggest cone area will be 125pi.

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subhash prasad saha  (9 years ago)

If can take min(12,10)/2 as radius and height as 15

So ans will be 125π

Is this solution Helpfull? Yes (2) | No   

sujit  (9 years ago)

12*15*11.6=2088

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Shernaz  (9 years ago)

12*10*15 = L*B*H..
1) Taking 12/2=6 as radius and cone will be formed in a vertical way. So height=15, volume of cone = 180pi

2) Taking 10/2=5 as radius and now cone will be formed in a horizontal way,So height=12, volume of cone = 100pi.

So case 1 is the biggest cone, So 180pi is the answer.

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suman kumar  (9 years ago)

three kind of bases are there (10,12) or (12,15) or(10,15);
thus radius and height can be paired as (5,15) or (6,10) or (5,12)
by considering all this surface with(10,12) has maximum volume;
thus,volume=(1/3)*pi*(r^2)*h=125*pi=392.7

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Mithun Kumar Kesari  (9 years ago)

check all cases
best case is
r=15/2
h=12
so, volume= 1/3*pi*r^2*h= 225 pi

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