Question

A solid cylinder of 16 cm diameter and 2 cm height was melted and 12 spheres of uniform sizes when made from it. The diameter of its sphere is

Answer 1

Formula used

• Volume of cylinder

$\pi r {}^{2} h$

Given,

r=16/2cm=8cm

h=2cm

Therefore

• Volume=
• $\pi \: \times 8 {}^{2} \times 2 = 128\pi \: cm {}^{2}$

Now lt the radius of the smaller one is a cm

Therefore as the larger one is melted to form 12 pieces of small one of same size so...

The height of the each smaller one will be =2cm

Therefore

Volume of the 12 such small cylinders and the larger cylinder will be equal

So

$12 \times \pi \times( a) {}^{2} \times h = \pi \times (r) {}^{2} \times h \\ a= \sqrt{ \frac{r {}^{2} }{12} } \\ diameter = 2a = 2 \sqrt{ \frac{r {}^{2} }{12} } \\ d = 2 \sqrt{ \frac{8 {}^{2} }{12} } \: cm \\ d = 2 \times 2.309 \\ d = 4.62 \: cm$

Answer

4.62 cm

Now it is melted to form 12 spheres

Let, Volume each of sphere =(4/3)pie *a^3

12*(4/3)pie *a^3=pie*r^2*h

a=[(r^2*h)/16]^(1/3)

a=[(64*2)/16]^(1/3)

a=[8]^(1/3)

a=2 cm

ANSWER

diameter of each sphere is =2*2cm=4cm