Question

A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively, is melted and recast in the form of a cone of base diameter 8 cm. The height of the cone is ______.

पर्याय

• 12 cm

• 14 cm

• 15 cm

• 8 cm

Answer 1

A metallic spherical shell of internal and external diameters 4 cm and 8 cm, respectively, is melted and recast in the form of a cone of base diameter 8 cm. The height of the cone is 14 cm.

Explanation:

Let the internal and external radii of the spherical shell be r and R, respectively.
Volume of the spherical shell`= 4/3pi("R"^3 - r^3)`

`=4/3 pi [(4)^3 - (2)^3] "cm"^3`     .....[since` "r" ⇒ 4/2 = 2 " cm". "R"= 8/2 = 4 " cm"`]

`= (4/3pixx56) "cm"^3`

Radius of the cone `= 8/2 = 4  "cm"`

Volume of the cone `=1/3 pi"r"^2"h"`

Therefore 

`1/3 pixx4xx4xx"h"xx = 4/3 pixx56`

`=> 16/3 xx "h" = 4/3pi xx 56`

`=> "h" = (4xx56xx3)/(3xx16)`

`=>"h" = 14  " cm"`