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.
Given,
Internal diameter of the hemisphere = 6 cm
External diameter of the hemisphere = 10 cm
Diameter of cone = 14 cm
So we have,
Internal radius(r) of the hemisphere = 3 cm
External radius(R) of the hemisphere = 5 cm
Radius of cone = 7 cm
Now,
Volume of the hollow hemisphere = Volume of the cone
Volume of the hollow hemisphere =
Volume of the cone =
So,
= 2 × 98 = 49 × h
= h
So,
h = = 4 cm
Thus, the height of the cone formed is 4 cm.