Question

How many lead balls of radius 2cm can be made from a ball of radius of 4cm ​

Answer 1

The Radius of Big Ball = R = 4cm

The radius of lead ball = r = 2 cm

Volume of Big Ball = 4/3πR³

Volume of Lead Ball = 4/3πr³

No. of Lead balls = Volume of Big Ball / Volume of One Lead Ball

= 4/3πR³ / 4/3πr³

= R³ / r³

= 4 × 4 × 4 / 2 × 2 × 2

= ( 2 × 2 × 2) = 8

So No. of Lead Balls = 8

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Answer 2

Answer:

Eight lead balls of radius 2cm can be made from one ball of radius of 4cm.​

Step-by-step explanation:

We have given, the radius of Big lead ball, R = 4cm

The radius of small lead ball , r = 2cm

Volume of a spherical ball $=\frac{4}{3}\pi r^3$

Therefore, the volume of big lead ball will be:

$V_{B}=\frac{4}{3}\pi R^3$

$V_{B}=\frac{4}{3}\pi (4)^3$                                                              ....................(1)

The volume of small lead ball will be:

$V_{s}=\frac{4}{3}\pi r^3$

$V_{s}=\frac{4}{3}\pi (2)^3$                                                               ...................(2)

We can calculate the total number of small lead balls made from big lead ball by dividing the volume of big ball to volume of small ball.

Number of small balls = Volume of big lead ball/Volume of small lead ball

Number of small lead balls  $=\frac{V_{B}}{V_{S}}$

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

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

$=\frac{64}{8}$

$=8$ small lead balls.

Therefore, 8 small lead balls of radius 2cm made from one big lead ball of radius 4cm.