Question

A cylinder of radius 2 cm and height 10 cm is melted into small spherical balls of diameter 1 cm. Find the number of such balls.

Answer 1

Volume of Cylinder V = π r^2 h

r= 2 cm, height = 10 cm

V = 125.7 cm^3 (approximate)

Volume of sphere V=4 /3πr^3

d = 1 cm, then r = 0.5 cm

V = 0.524 cm^3 (approximate)

Required no. of spherical balls =

$\frac{Volume of cylinder}{volume of spherical ball}$

= 125.7/0.524

= 240

Answer 2

Solution :

i ) dimensions of the cylinder:

Radius = R = 2 cm

Height = h = 10 cm

ii ) dimensions of the sphere:

Diameter ( d ) = 1 cm

Radius of each small sphere (r)

r = d/2 = 1/2 cm

NOW ,

If cylinder melted and cast

into small spheres ,

Let the number of spheres = n

n = ( volume of cylinder)/volume of each sphere )

n = ( πR²h )/[ (4/3)πr³ ]

=> n = (3 R²h )/( 4r³ )

=> n = ( 3×2×2×10)/[4×(1/2)³]

=> n = (3×10×2³)

=> n = 240

Therefore ,

Number bof small spheres = 240

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