Question

The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm, respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.

Answer 1

Internal diameter of the hemispherical shell = 6 cm
Therefore, internal radius of the hemispherical shell = 3 cm

External diameter of the hemispherical shell = 10 cm
External radius of the hemispherical shell = 5 cm

Volume of hemispherical shell `= 2/3 pi (5^3 -3^3) = 196/3xx22/7=616/3  "cm"^3`

Radius of cone = 7 cm

Let the height of the cone be h cm.

Volume of cone =` 1/3pir^2h = 1/3xx22/7xx7xx7h= (154h)/3 "cm"^3`

The volume of the hemispherical shell must be euqal to the volume of the cone therefore

`(154h)/3 = 616/3`

`rArr h = 616/154 =4  "cm"`