Question

A metallic sphere of radius 6 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.​

Answer 1

Answer:

V(sp) = V(cyl)

4/3*pi*r,³ = pi*r²*h

4/3 * 6³ = 6²*h

=> 4/3 * 6 = h

=> h = 8 cm

Answer 2

Given :

• A metallic sphere of radius 6 cm is melted.

• The shape of a cylinder of radius 6 cm.

To find :

• The height of the cylinder =?

Step-by-step explanation :

Since sphere is melted into a cylinder.

So, Volume os sphere = Volume of cylinder

Volume of sphere,

Radius, r = 6 cm

We know that,

Volume of sphere = 4/3 π r³

Substituting the values in the above formula, we get,

= 4/3π(6) ³

Volume of cylinder,

Radius, r = 6 cm

Let, height = h cm.

We know that,

Volume of cylinder = πr²h

Substituting the values in the above formula, we get,

= π (6)² h

= 36πh

Now,

Volume of sphere = Volume of cylinder

Substituting the values, we get,

4/3π(6)³ = 36πh

4/3π(6)³× 1/3π = h

h = 4/3π(6)³ × 1/36π

h = 4/3(6)³ × 1/36

h = 4/3 × 6 × 6 × 6 × 1/36

h = 6 × 6 × 6/27

h = 6 × 6 × 6/3 × 3 × 3

h = 2 × 2 × 2

h = 8.

Therefore, Height of cylinder = 8 cm.