Question

A solid metallic cylinder of radius 3.5 cm and height 14 cm is melted and recast into a number of small solid metallic balls each of the radius 7 by 12 cm find the number of balls so formed

Answer 1

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Answer 2

Answer:

648 balls can be formed.

Step-by-step explanation:

Given : A solid metallic cylinder of radius 3.5 cm and height 14 cm is melted and recast into a number of small solid metallic balls each of the radius 7 by 12 cm.

To find :  The number of balls so formed?

Solution :  

Radius of cylinder R =3.5 cm

Height H =14cm

Volume of cylinder,

$V=\pi r^2 h$  

$V=\pi\times 3.5^2\times 14$  

$V=171.5\pi$  

Radius of the ball $r=\frac{7}{12} cm$

Volume of sphere,

$V=\frac{4}{3}\pi r^3$  

$V=\frac{4}{3}\pi\times \frac{7}{12}^3$  

$V=\frac{343}{1296}\pi$

$V=0.2646\pi$  

Number of balls made,

$n=\frac{\text{Volume of cylinder}}{\text{Volume of sphere}}$

$n=\frac{171.5\pi}{0.2646\pi}$

$n=648.148$

Therefore, 648 balls can be formed.