Latest Elitmus Aptitude Question SOLUTION: A solid rightcircular cone has a radius of 6cm and height 1cm. what is the maximum possible volume of a solid cylinder cut from that cone?

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(#M40019211) ELITMUS Numerical Ability question Keep an EYE

A solid rightcircular cone has a radius of 6cm and height 1cm. what is the maximum possible volume of a solid cylinder cut from that cone?

Asked In Elitmus Prakash Gupta (10 years ago)

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Mohit Awasthi  (10 years ago)

Express the height in terms of the radius.
Since h=1, r=6

h = (1 – r/6)

V = πr²h
V = πr²(1 – r/6)
V = πr² - πr³/6
dV/dr = 2πr - (3/6)πr²

Let dV/dr = 0
2πr - (1/2)πr² = 0
2r –(1/2) r² = 0
r = 0 &,
r = 4 ............... Reject r = 0.

V = πr²(1 – r/6)
V = 16π/3 cm³

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sanjay  (10 years ago)

the formula to find the highest possible volume of a cylinder inscribed inside a cone is V = pi*(r^2)*h*(4/27)
so r=6 and h=1
therfore V= pi*(6*6)*1*(4/27)=(16/3)*pi

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shailesh  (10 years ago)

@mohit h=(1-r/6)=0, r=6

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Shubhanshu  (10 years ago)

I am moving this to calculus since it is more of a calc problem.

Let R and H be the radius and height of the cone, and r and h be the radius and height of the cylinder.

The volume of the cylinder is V={pi}r^{2}h

Now, as in a lot of these problems, use similar triangles.

frac{H-h}{H}=frac{r}{R}

Therefore, h=frac{H}{R}(R-r)

Plug this into the cylinder volume equation at the top. H and R are given constants.

Then differentiate to find dV/dr. Set to 0 and solve for r.

If done correctly, you should find that the volume of the cylinder that has max volume is 4/9 the volume of the cone.

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ranjeet singh chauhan  (10 years ago)

@awasthi... kahn s mila yar y...solution ?

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