Question

A solid sphere of diameter 18 cm is melted and 24 long cylinder is formed.find its diameter.

Answer 1

Given

Dia of sphere=18cm

Radius of the sphere =18/2 =9cm

First of all let calculate volume of the sphere because in question it is given that the sphere is melted and moulded in cylinder shape

Which means volume of sphere will be equal to volume of the cylinder.

$Volume \: of the \: sphere \: = \frac{4}{3} \pi {r}^{3}$

$= \frac{4}{3} \times \frac{22}{7} \times {9}^{3}$

=64152/21 cm³

Now volume of the sphere = volume of the cylinder =64152/21cm³

And we know volume of the cylinder =
$= \pi \: {r}^{2} h$

H=24cm

$\frac{22}{7} \times {r}^{2} \times 24 = \frac{64152}{21}$

${r}^{2} = \frac{64152 \times 7}{21 \times 22 \times 24}$

${r}^{2} = 40 .5$
$r = \sqrt{40.5}$

R=6.3639cm

Dia of the cylinder =6.3639x2

=12.728cm

Short way

Volume of sphere = volume of cylinder

4/3 pi r³ = pi R² h

Pi cancel both side we left with

4/3 r³ = R² h

4/3 (9)³= R² x24

4/3 x 729 = R² x 24

R²= 40.5

R=6.3639cm

D=12.728cm

This is your ans hope it will help you in case of any doubt comment below

Answer 2

According to question we have given diameter of sphere = 18 cm.
Then radius of sphere = 9 cm
Also, we have given height of cylinder = 24 cm.
We have to find the radius of cylinder = ?
Volume of sphere = 4/3 π r³
Volume of cylinder = π r²h
Now,
A.T.Q,Volume of sphere = Volume of cylinder
4/3 π r³ = π r² h
4 x 22 x 9 x 9 x 9 = 22/7 x r x 24
______________
3 x 7

On solving we get,
r² = 40.5
Then,
r = 6.36
Now,
Diameter of cylinder = 6.36 x 2 = 12.72

Hope it helps you.