Question

The diameter of the internal and external
surfaces of hollow hemispherical shell
are 6cm & 10cm respectively It is melted
and recasted into a solid cylinder of
diameter 14cm find the height of the
cylinder.​

Answer 1

Answer:

4/3 cm or 1.33 cm

Step-by-step explanation:

( Refer to attachment for the figure )

Diameter of the internal surface of the hollow hemisphere = 6 cm

Radius of the internal surface of the hollow hemisphere ( R ) = 6/2 = 3 cm

Diameter of the external surface of the hollow hemisphere = 10 cm

Radius of the external surface of the hollow hemisphere = 10/2 = 5 cm

Diameter of the base of the solid cylinder = 14 cm

Radius of the base of the solid cylinder ( r' ) = 14/2 = 7 cm

Let the height of the solid cylinder be 'h' cm

Given :

Hollow hemispherical shell is melted and recasted into solid cylinder

⇒ Volume of the solid cylinder = Volume of the hollow hemispherical shell

We know that :

• Volume of the solid cylinder = πr²h sq.units
• Volume of the hollow hemisphere = Volume of the external hemisphere - Volume of internal hemisphere

⇒ πr'²h = 2/3 πR³ - 2/3 πr³

Dividing by π on both sides

⇒ r'²h = 2/3 ( R³ - r³ )

⇒ 7² × h = 2/3 ( 5³ - 3³ )

⇒ 49h = 2/3 ( 125 - 27 )

⇒ 49h = 2/3 × 98

⇒ 49h = 196/3

⇒ h = 196/( 49 × 3 )

⇒ h = 4/3

⇒ h = 1.33

Therefore the height of the cylinder is 4/3 cm or 1.33 cm.