Question

a metallic cylinder of diameter 5 cm and height 10/3 cm is melted and cast into sphere. what is its diameter

Answer 1

Solutions :-

Given :
Diameter of the metallic cylinder = 5 cm
Radius of the metallic cylinder = r = 5/2 = 2.5 cm
Height of the metallic cylinder = 10/3 cm


Find the volume of cylinder :-

Volume of cylinder = πr²h cu. unit
= 22/7 × (2.5)² × 10/3
= 65.48 (approx)


Now,
A metallic cylinder is melted and cast into sphere.

Find the radius of sphere :-

Volume of sphere = 4/3πr³

=> 65.48 = 4/3 × 22/7 × r³
=> 65.48 × 3 × 7 = 4 × 22 × r³
=> 1375 (approx) = 88r³
=> r³ = 1375/88 = 15.625
=> r = 3√15.625 = 2.5


Diameter = Radius × 2 = 2.5 × 2 = 5 cm


Hence,
Diameter of sphere = 5 cm


_______________________

✯ @shivamsinghamrajput ✯

Answer 2

Answer:

The diameter of the the sphere is 5 cm.

Step-by-step explanation:

It is given that a metallic cylinder of diameter 5 cm and height 10 / 3 cm is melted and cast into a sphere.

We know that if we cast anything from one state to other, it's volume can't be change.

So,

⇒ Volume of metallic cylinder = Volume of sphere

We know,

Volume of cylinder = πr^2h

And, volume of sphere = 4 / 3 πr^3

Now, let the radius of sphere be a,

Radius of the cylinder = diameter / 2 = 5 cm / 2 = 2.5 cm

= >  π( 2.5 )^2 x ( 10 / 3 ) = 4 / 3 π x r^3

= >  ( 2.5 )^2 x 10 / 3 = 4 / 3 x r^3

= >  ( 2.5 )^2 x 10 = 4 x r^3

= >  ( 2.5 )^2 x 10 / 4 = r^3

= >  6.25 x 5 / 2 = r^3

= >  15.625 = r^3

= >  ∛15.625 = r  

= >  2.5 = r

= >  2 x 2.5 cm = 2 x r

= >  5 cm = diameter

Therefore the diameter of the the sphere is 5 cm.