Question

A cylinder of radius 12 cm and height 16 cm is melted and the same mass is used to create a sphere. What
will be the radius of the sphere?

Answer 1

⇒ Final Answer:

12 cm

⇒ Given:

Radius of cylinder = 12 cm

Height = 16 cm

⇒ To Find:

Radius of the sphere

⇒ Analysis:

In this question, we first have to find the volume of the cylinder from the given measures. Then we can give the same volume for the sphere as the same cylinder is remolded to form a sphere. Then we can find the radius of the sphere from the volume.

⇒ Formulae to be used:

→ $\boxed{\sf{Volume\:of\:cylinder=\pi\:r^2h}}$

→ $\sf{\boxed{\sf{Volume\:of\:sphere=\dfrac{4}{3}\pi\:r^3}}}$

⇒ Solution:

First we need to find the volume of the cylinder:

Height of the cylinder = 16 cm

Radius = 12 cm

Volume of cylinder = πr²h

$\sf{=\dfrac{22}{7}\times12\times12\times16}$

$\sf{=\dfrac{50688}{7}}$

Now, we know that:

Volume of cylinder = Volume of sphere

Hence,

Volume of sphere = 50688/7 ------ (1)

Formula for sphere = 4/3πr³ ------ (2)

Combining equations (1) and (2):

$\sf{=\dfrac{4}{3}\times\dfrac{22}{7}\times\:r^3=\dfrac{50688}{7}}$

$\sf{=r^3=\dfrac{50688}{7}\times\dfrac{3}{4}\times\dfrac{7}{22}}$

$\sf{=r^3=1728}$

$\sf{r=12\:cm}$

Hence the radius of the sphere is 12 cm.