Question

If circular metal sheet is 0.65cm thick and of 50cm in diameter is melted and recast into cylindrical bar with 8cm diameter then the length of bar is

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.)

                                                                           

Answer 2

Step-by-step explanation:

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}

100

65

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

2

Diameter

= \frac{50}{2}

2

50

= 25 cm.

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

2

h

= \pi 25^{2}\frac{65}{100}π25

2

100

65

cm^{3}cm

3

Let, Height of the cylindrical bar is (H)

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

2

Diameter

= \frac{8}{2}

2

8

=4 cm

Therefore, Volume of the cylindrical bar = \pi R^{2} HπR

2

H = \pi 4^{2}Hπ4

2

H cm^{3}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}π25

2

100

65

= \pi 4^{2} Hπ4

2

H

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

4

2

25

2

100

65

=25.390625 cm = 25.39 cm (approx.)