Question

(c) A solid cylinder of radius 7 cm and height 14 cm is melted and recast into solid
spheres each of radius 3.5 cm. Find the number of spheres formed.

Answer 1

vol. of cylinder = 22/7 * r * r * h
                        = 22/7 * 7 * 7 * 14
 
vol. of sphere   = 4/3*22/7*3.5*3.5*3.5

vol. of cylinder = vol. of sphere * n       (n = no . of spheres)
22/7*7*7*14     =   4/3*22/7*3.5*3.5*3.5
                 n     = 12
therefore ,
                 12 spheres can be made from the cylinder . 

Answer 2

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Let radius of cylinder=r
and height of cylinder=h
and radius of sphere be R

Suppose no. of spheres are x
Now,
Vol. of the cylinder= No. of spheres×Vol. of 1 sphere
pi×r²×h=x×4/3×pi×R³
r²×h=x×4/3×R³
7×7×14=x×4/3×3.5×3.5×3.5
x=12
Hence,
No. of spheres=12


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