Question

An aluminium sphere of radius 12 cm is melted to make a cylinder of radius 8 cm
Find the height of the cylinder.
through a nine of diameter 14 sm into a​

Answer 1

Given,

An aluminum sphere of radius 12 cm is melted to make a cylinder of radius 8 cm .

To find :

Find the height of the cylinder.

Solution :

Radius of sphere , r = 12 cm

Radius of cylinder, R = 8 cm

As aluminum sphere is melted to make the cylinder, so :

⇒ Volume of sphere = Volume of cylinder

Now we know,

Volume of sphere = 4/3 πr³

Volume of cylinder = πr²h

Now atq,

⇒ 4/3 πr³ = πR²h

⇒ 4/3 * π(12)³ = π(8)²h

⇒ 4/3(1728) = 64h

⇒ 4 * 576 = 64h

⇒ 2304 = 64h

⇒ h = 2304/64

⇒ h = 36 cm

Therefore,

Height of the cylinder = 36 cm.

Answer 2

Answer:

Given :-

• An aluminium sphere of radius 12 cm is melted to make a cylinder of 8 cm.

To Find :-

• What is the height of the cylinder.

Solution :-

Given :-

• Radius (r) = 12 cm
• Radius (R) = 8 cm

First, we have to find the Volume of sphere,

$\boxed{\bold{\small{Volume\: of\: Sphere\: = \dfrac{4}{3} \pi{r}^{3}}}}$

Now,

⇒ Volume of sphere = $\dfrac{4}{3}$ × $\dfrac{22}{7}$ × 12 × 12 × 12

⇒ Volume of sphere = $\dfrac{50688}{7}$

Again, we know that,

$\boxed{\bold{\small{Volume\: of\: sphere\: =\: Volume\: of\: cylinder}}}$

According to the question by using the formula we get,

Volume of Cylinder = πR²h

⇒ $\dfrac{50688}{7}$ = $\dfrac{22}{7}$ × (8)² × h

⇒ 50668 × $\dfrac{7}{7}$ × 22 × 64 = h

⇒ $\dfrac{50668}{22}$ × 66 = h

⇒ $\dfrac{2304}{64}$ = h

⇒ 36 = h

➠ h = 36

∴ The height of the cylinder is 36 cm .