Latest Elitmus Aptitude Question SOLUTION: Cone of base radius 1m, height 6m. What is the maximum volume of cylinder can be formed by this cone.

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(#M40038374) ELITMUS Logical Reasoning question Keep an EYE

Cone of base radius 1m, height 6m. What is the maximum volume of cylinder can be formed by this cone.

Asked In Elitmus Ritesh Anand (9 years ago)

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Sujoy Das  (9 years ago)

Let the radius of cylinder=x;height of cylinder=h;
y is the length from vertex of the cone to the top surface of the cylinder
y/x=6/1;
Volume of cylinder=pi*x^2*h;
h=6-(6*x);
Volume=pi*x^2*(6-(6*x))
Now to get the maximum volume we have to differentiate Volume with respect to x
6*pi[2x-3x^2]=0;
x=2/3;
Therefore h=6-6*2/3;
h=2;
Volume=pi*(2/3)^2*2;
Volume=8pi/9;

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Sujoy Das  (9 years ago)

Let the radius of cylinder=x;height of cylinder=h;
y is the length from vertex of the cone to the top surface of the cylinder
y/x=6/1;
Volume of cylinder=pi*x^2*h;
h=6-(6*x);
Volume=pi*x^2*(6-(6*x))
Now to get the maximum volume we have to differentiate Volume with respect to x
6*pi[2x-3x^2]=0;
x=2/3;
Therefore h=6-6*2/3;
h=2;
Volume=pi*(2/3)^2*2;
Volume=8pi/9;

You can also check it here
http://www.mathalino.com/reviewer/differential-calculus/cylinder-maximum-volume-and-maximum-lateral-area-inscribed-cone

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subhash kumar  (9 years ago)

ans: 2 pie

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Vishwash Kumar Singh  (9 years ago)

6pie , Because volume of cylinder pie*r^2*h

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arjun kumar jha  (9 years ago)

ans is 9pie/4
cylinder will reach its max volume when the height of cylinder will be half of the height of cone....if we consider that,we will be able to see the radius of cylinder becoming half of the radius of cone....volume of cylinder will be pie*1/2*1/2*3

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raushan kumar  (9 years ago)

1-h/1 = r/6 h = hight of cylinder , r = radius of cone.(using ~ triangle concept)

h = 1-r/6

dV/dr=0, v= 1/3*pi*r^2*(1-r/6) (V of cone)
r=4 , h= 1/3.

then volume of cyl. = pi*r^2*h = Pi*16/3.

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abhishek  (9 years ago)

hii i want to know r sat exam fee and is this exam held in delhi online test or pen paper test and the pattern of this exam plz tell me in detail
Read more at http://www.m4maths.com/placement-puzzles.php?SOURCE=R-SAT#4vBcJp8pzYBLmRRT.99

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hari prasad  (9 years ago)

How do we valuate h=6-(6*x);

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