Question

How many spherical balls can be made out of a solid cube of lead whose edge measures 44 cm and each ball being 4 cm. in diameter.

Answer 1

Hi ,

i ) Dimensions of the solid lead cube :

edge of the cube ( a ) = 44 cm

volume of the cube ( V1 ) = a³ ---( 1 )

ii ) Dimensions of the each Spherical ball :

diameter ( d ) = 4cm

radius ( r ) = d/2 = 4/2 = 2 cm

volume of the each ball ( V2 ) = ( 4/3 )πr³--(2 )

Let the number of spherical balled made

by the solid cube are ' n '

n = ( V1 )/( V2 )

n = ( a³ )/[ ( 4/3 )πr³ ]

n = ( 44 )³ /[ ( 4/3 )× ( 22/7 ) × 2³ ]

n = ( 44 × 44 × 44 × 7 )/( 3 × 22 × 8 )

n = ( 1788864 )/( 704 )

n = 2541

Therefore ,

2541 Spherical balls are made from the

given Solid cube .

I hope this helps you.

: )

Answer 2

Answer:

2543 balls were required.

Step-by-step explanation:

Given : A solid cube of lead whose edge measures 44 cm and each ball being 4 cm. in diameter.

To find : How many spherical balls can be made out of a solid cube?

Solution :

Dimensions of the solid lead cube,

Edge of the cube a= 44 cm

Volume of the cube $V=a^3$

$V=44^3=85184cm^3$

Dimensions of the each Spherical ball,

Diameter d= 4cm

Radius r= 2 cm

Volume of the each ball $v=\frac{4}{3}\pi r^3$

$v=\frac{4}{3}(3.14) 2^3$

$v=\frac{4}{3}(3.14)(8)$

$v=33.493cm^3$

Let the number of spherical balled made by the solid cube are ' n '

$n=\frac{V}{v}$

$n=\frac{85184}{33.493}$

$n=2543.3$

Therefore, Approximately 2543 balls were required.