Question

a solid metal ball of radiud 8 cm is metaled and cost into smaller balls each of radius 2 cm the number of such balls is ​

Answer 1

GIVEN :-

• Radius of the larger solid metal ball , R = 8 cm

• Radius of the smaller solid metal ball , r = 2 cm

TO FIND :-

• Number of small solid balls .

SOLUTION :-

   Let the number of balls = x

 

     $\bf Volume \ of \ sphere = \dfrac{4}{3} \pi r^3$

  Volume of the larger metal ball ,

   $\longrightarrow \sf \dfrac{4}{3} \pi R^3 \\\\\longrightarrow \dfrac{4}{3} \times \pi \times 8 \times 8 \times 8$

  Volume of the smaller ball ,

   $\longrightarrow \sf \dfrac{4}{3} \pi r^3 \\\\\longrightarrow \dfrac{4}{3} \times \pi \times 2 \times 2 \times 2$

 According to the question ,

 Volume of the larger metal ball = x × Volume of the smaller ball

$\longrightarrow\sf \dfrac{4}{3} \times \pi \times 8 \times 8 \times 8 =x \times \dfrac{4}{3} \times \pi \times 2\times 2 \times 2 \\\\\longrightarrow 8 \times 8 \times 8 = x \times 2\times 2 \times 2 \\\\\longrightarrow x = \dfrac{8\times 8\times 8 }{2 \times 2 \times 2 }\\\\\longrightarrow x = 4\times 4\times 4\\\\\longrightarrow x = 64$

Number of small balls = 64

Answer 2

Correct Question : A solid metal ball of radius 8 cm is melted and cast into smaller balls, each of radius 2 cm. The number of such balls is ?

Answer:

The number of smaller balls will be 64.

Step-by-step explanation:

• Radius of the single solid metal ball = 8 cm.

• Radius of the each smaller solid balls = 2 cm

Let the Number of ball be x.

Now, According to question :

Volume of metal ball = No. of metal balls × Volume of one ball

4/3 πr³ = x (4/3 πr³)

r³ = x (r)³

8³ = x (2)³

x = 8×8×8/2×2×2

x = 64