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

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
9 years agoHelpfull: Yes(3) No(2)
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.
9 years agoHelpfull: Yes(3) No(1)
If can take min(12,10)/2 as radius and height as 15

So ans will be 125π
9 years agoHelpfull: Yes(2) No(0)
12*15*11.6=2088
9 years agoHelpfull: Yes(0) No(0)
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.
9 years agoHelpfull: Yes(0) No(2)
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
9 years agoHelpfull: Yes(0) No(0)
check all cases
best case is
r=15/2
h=12
so, volume= 1/3*pi*r^2*h= 225 pi
9 years agoHelpfull: Yes(0) No(1)

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