Question

If circular metal sheet is 0.65cm thick and of 25cm in radius is melted and recast into cylindrical bar with 4cm radius, then what will be the length of bar ?

Answer 1

Answer:

   Length of the cylindrical bar is 25.39 cm. (approx.)

Step-by-step explanation:

Thick / Height (h) of the circular metal sheet is 0.65 cm. = \frac{65}{100}

Radious (r) of the sheet = \frac{Diameter}{2}

                                  = \frac{50}{2} = 25 cm.

Therefore, volume of the circular metal sheet = \pi r^{2}h

                                                                          = \pi 25^{2}\frac{65}{100} cm^{3}

Let, Height of the cylindrical bar is (H)

Radious (R) of the base of cylindrical bar = \frac{Diameter}{2}  = \frac{8}{2} =4 cm

Therefore, Volume of the cylindrical bar = \pi R^{2} H = \pi 4^{2}H cm^{3}

Since, circular metal sheet is melted and recast into cylindrical bar

So,

   volume of the circular metal sheet = Volume of the cylindrical bar

⇒ \pi 25^{2}\frac{65}{100}      =    \pi 4^{2} H

⇒H= \frac{25^{2}\frac{65}{100} }{4^{2} }  =25.390625 cm = 25.39 cm (approx.)