Question

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

Answer 1

Answer:

the no. of small spherical balls = 75

Step-by-step explanation:

For soid sphere,

Radius ( R ) = 3 cm

.°. Volume = $\frac{4}{3}$ × π ×${R}^{3}$

= $\frac{4}{3}$π × ${3}^{3}$ ${cm}^{3}$

= $\frac{4}{3}$ × π × 27 ${cm}^{3}$

= 36π ${cm}^{3}$

Now,

for small spherical balls,

Diameter (d)= 0.6 cm

=> radius (r) = $\frac{d}{2}$= $\frac{0.6}{2}$= 0.3 cm

so,

volume (${V}^{'}$ ) = $\frac{4}{3}$π${r}^{3}$

= $\frac{4}{3}$ × π× ${(0.3)}^{3}$${cm}^{3}$

= $\frac{4}{3}$ × π × 0.027 ${cm}^{3}$

= 0.036 π ${cm}^{3}$

Now, it is given that

the solid sphere was melted to form these small spherical balls

So, it is must that the volume of solid sphere equals to the sum of volumes of all small spherical balls

or, we can say that

V = n ${V}^{'}$

where, n is the no. of small spherical balls

Here, n times is used because the volume of every single small spherical balls is same.

=> n = $\frac{V}{V'}$

=> n = $\frac{27π}{0.36π}$

=> n = $\frac{2700π}{36π}$

=>n = $\frac{2700}{36}$

=> n = 75

So, the no. of small spherical balls = 75

Answer 2

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