Question

A solid sphere of radius 3 cm is melted and recast into small spherical balls and each of diameter 0.6 m find the number of moles

Answer 1

A solid sphere of radius 3 cm is melted and recast into small spherical balls and each of diameter 0.6 cm. Find the number of spherical balls.

Step by step explanation :

Given :

Radius of the solid sphere = 3 cm

Diameter of small balls = 0.6 cm

We know that, Diameter = 2 r

0.6 = 2 r , r = 0.3 cm

Now,

Volume of Sphere = 4/3 π r^3

We have to find number of ( small ) balls :

$\tt \small{Number \: of \: small \: balls = \frac{Volume \: of \: Sphere }{Volume \: of \: small \: balls}}$

$\tt{= \frac{ \frac{4}{3} \times 3.14 \times (3) {}^{3} }{ \frac{4}{3} \times 3.14 \times (0.3) {}^{3}} }$

$\tt{= \frac{ \cancel \frac{4}{3} \times \cancel{3.14}\times (3) {}^{3} }{ \cancel\frac{4}{3} \times \cancel{3.14} \times (0.3) {}^{3}} }$

Thus, We get :

$\tt {= \frac{3 {}^{3} }{0.3 {}^{3}} }$

3^3 = 3 × 3 × 3 ,

0.3^3 = 0.3 × 0.3 × 0.3

Thus,

$\tt{= \frac{3 \times 3 \times 3}{0.3 \times 0.3 \times 0.3}}$

$\tt { \tt{= \frac{27}{0.027} = 1000}}$

(0.027 × 1000 = 27)

So, It means that there are total 1000 small balls.

Final Answer :

There are 1000 small balls.

________________________

Answer 2

$\underline{\mathfrak{\huge{Question:}}}$

A solid sphere of radius 3 cm is melted and recast into small spherical balls and each of diameter 0.6 cm. Find the number of balls.

$\underline{\mathfrak{\huge{Answer:}}}$

Let the radius of the bigger sphere be = R
And the radius of the smaller sphere be = r

$\sf{We're\:Given\:that:-}$

R = 3 cm

d = 0.6 cm

r = $\tt{\frac{d}{2}}$

=》 r = 0.3 cm

Number of balls = $\tt{\frac{Volume\:of\:bigger\:sphere}{Volume\:of\:smaller\:sphere}}$

● Volume of bigger sphere = $\tt{\frac{4}{3} \pi R^{3}}$

=》 Volume = $\tt{\frac{4}{3} \times \frac{22}{7} \times{3}^{3}}$

=》 Volume = $\tt{\frac{4 \times 22 \times 9}{7}}$

● Volume of smaller sphere = $\tt{\frac{4}{3} \pi r^{3}}$

=》 Volume = $\tt{\frac{4}{3} \times \frac{22}{7} \times{0.3}^{3}}$

=》 Volume = $\tt{\frac{4 \times 22 \times 9}{7 \times 1000}}$

Divide them, and there'll be your answer !

Number of balls =》 $\tt{\frac{4 \times 22 \times 9}{7} \times \frac{7 \times 1000}{4 \times 22 \times 9}}$

Doing the necessary operations, we get :-

=》 Number of balls = $\tt{1000}$