Question

A spherical lead of radius 8 cm is melted and small lead balls of radius 16 mm are made. The total number of possible small lead balls is:​

Answer 1

What's the Question about?

• The above question is a simply based on mensuration/ volume of spheres. Here, we have to find the volume of bigger sphere and divide it by the volume of smaller sphere.

Required Answer:

We have:

Radius of spherical lead = 8 cm

Radius of small balls = 16 mm = 1.6 cm

To FinD:

Total no. of small lead balls?

Step-by-step calculation:

No. of small lead balls:

$= \sf\dfrac{ volume \: of \: larger \: sphere}{volume \: of \: small \: balls}$

We know that, Volume of a sphere is given by: 4/3 πr³ where r is the radius of the sphere.

Plugging the values:

No. of small lead balls:

$\large= \sf{ \dfrac{ \dfrac{4}{3}\pi(8) {}^{3} }{ \dfrac{4}{3} \pi {(1.6)}^{3} } }$

$\large= \sf{ \dfrac{8 \times 8 \times 8}{1.6 \times 1.6 \times 1.6} }$

$\large = \sf{5 \times 5 \times 5 }$

$\large = \sf{125 \: balls}$

Hence,

The total number of possible small lead balls is: 125 balls. And we are done! :D

Note!!

Whenever you are solving some questions similar to this, don't calculate the values at the beginning. Because they can be cancelled out easily in later steps like we did in this one.

Answer 2

Answer is 125

Radius of spherical lead = 8 cm

Radius of small balls = 16 mm = 1.6 cm

Total no. of small lead balls?

First we will find volume of a sphere

=4/3(pi r^3)

Putting values

=(4/3)(pi×8^3)

Volume of small lead balls =(4/3)(pi ×1.6^3)

Now divide both volumes it will be equal to no of lead balls

=volume of original lead/volume of melted small lead

=8×8 ×8 /1.6×1.6×1.6

=125