Question

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is ______.

Options

• 2.1 cm

• 1.05 cm

• 1.5 cm

• 2 cm

Answer 1

A metallic cone having base radius 2.1 cm and height 8.4 cm is melted and moulded into a sphere. The radius of the sphere is 2.1 cm.

Explanation: 

Radius of cone = 2.1 cm

Height of cone = 8.4 cm

Volume of cone `= 1/3 pi"r"^2"h" = 1/3pi (2.1)^2xx8.4` 

`"Volume of the sphere" = 4/3 pi"r"^3`

Therefore,

Volume of cone = Volume of sphere

`=> 1/3pixx(2.1)^2xx8.4=4/3pi"r"^3`

⇒ 4.41 × 8.4 = 4r³ 

⇒ 37.044 = 4r³ 

`=> "r"^3 = 37.044/4`

⇒ r³ = (2.1)³