A castle has a pillar, which is a cylinder in shape with a cone of same base radius surmounted on it. The total height of the pillar is 60m and radius of the pillar is 5m. Find the height of the conical part, if the volume of the material used in making of pillar is 4400m^3.

Answer:
    Given radius of cylinder = 5 m
So,                
   Radius of cone  = 5 m                               (same base)
   Height of total  = 60 m
​   Volume of piller = 4400 $m^3$
Let,
   Height of cone = h m
​So,
  Height of cylinder part of the pillar = 60 - h
We know,
 Volume of cylinder part of pillar + Volume of cone part of pillar = 4400 $m^3$
 $\pi r^{2}h + \frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$ = 4400
 ${\mathrm{\pi r}}^2\left(60-\mathrm{h}+\frac{\mathrm{h}}{3}\right)$  = 4400
${\mathrm{\pi r}}^2\left(180 - 3\mathrm{h} +\mathrm{h}\right) = 4400\times 3$
180 - 2h = $\frac{13200}{\mathrm{\pi }\times 5\times 5}$
180 - 2h = $\frac{13200}{78.5714285714}$
180 - 2h = 168
     $\Rightarrow$2h = 180 - 168
     $\Rightarrow$2h = 12
     $\Rightarrow$h   = 6 m                          (Ans)
   

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