Question

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

Answer 1

Diameter of the metallic cylinder = 5 cm 

Radius = 5/2 = 2.5 cm

Height of the metallic cylinder = 3 1/3 cm = 10/3 cm

Volume of the metallic cylinder = πr²h

⇒ 22/7*2.5*2.5*10/3

⇒ 1375/21

Volume of the metallic cylinder = 65.476 cu cm

The metallic cylinder is melted and cast into a sphere. So, the volume of the metallic cylinder and the sphere will exactly same.

Volume of sphere = 4/3πr³

⇒ 65.476 = 4/3*22/7*r³

⇒ 88r³ = 65.476*21

⇒ 88r³ = 1374.996 or 1375 (Approx)

⇒ r³ = 1375/88

⇒ r³ = 15.625

⇒ r = ∛15.625

⇒ r = 2.5 

Hence, the radius of the sphere is 2.5 cm.

Then, diameter of the sphere = 2.5*2

= 5 cm

Answer 2

There is a basic thing you need to know that if volume of sphere always remains same when melted and changes its shape .
Volume of cylinder = volume of sphere
4/3 π r²h = 4/3 π r³
h = 4/3 π
r = 3/4 h
r = 3/4 * 10/3
r = 10/4
= 2.5