A hemisphere of lead of radius 8 cm is cast into a right circular cone of base radius 6 cm. Determine the height of the cone correct to 2 places of decimal.

A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

The entire surface of a solid cone of base radius 3 cm and height 4 cm is equal to entire surface of a solid right circular cylinder of diameter 4 cm. Find the ratio of their

(i) curved surfaces

(ii) volumes.

A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. Find the radius of the sphere.