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Sudhanshu Shekhar

· started a discussion

· 1 Months ago

problem (Question: 89869.0 )

what is k here...??
where did it come from..???

Question:
A solid sphere of radius 7 cm is melted to form a number of small cones and cylinders. The requirement is such that the number of cones should be twice the number of cylinders. Also the radius of the cone must be equal to its height, which should be equal to the radius of the cylinder and also be half the height of the cylinder. If the height of one such cylinder is 4 cm, find the maximum number of cones which can be made out of the sphere
Options:
A) 18
B) 21
C) 36
D) 42
E) None of these
Solution:
Volume of sphere = \(\cfrac{4}{3}π×r^3\)

Let the number of cylinders be k. Then, 2k is the number of cones.

Also

Rcylinder = Rcone= Hcone =  \(\cfrac{1}{2}\) Hcylinder = 4

\(⇒ \cfrac{4}{3} π×7^3=k (π×2^2×4)+2k\left ( \cfrac {1}{3}π×2^2×2 \right )\)

\(⇒k=\cfrac{7^3}{16}=21.4375\simeq21\)

So, number of cones = 42.

Anjuman Tiwari

· commented

· 1 Months ago

we have assumed that there are k cylinders of given height
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