Water is being poured into a vessel in the form of an inverted right circular cone of semi vertical angle `45^@` in such a way that the rate of change of volume at any moment is proportional to the area of the curved surfaces which is wet at that moment.Initially the vessel is full to a height of 1 cm and after 1 second the height is 3 cm.Show that the height of the water after 3 seconds will be 7 cm.

Water is being poured into a vessel in the form of an inverted right circular cone of semi vertical angle 45^@ in such a way that the rate of change of volume at any moment is proportional to the area of the curved surfaces which is wet at that moment.Initially the vessel is full to a height od 2 cm,after 2 seconds the height becomes 10 cm.Show that after 3.5 seconds from the start,the height of water will be 16 cm.

Find the volume of a right circular cone if r = 14 cm and h = 9 cm.

The slant side of a right circular cone is l. Show that the semi vertical angle of the cone of maximum volume is tan^(-1) ( sqrt 2 )

Find the volume of cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

The base radii of two right circular cones of the same height are in the ratio 2: 3. Find ratio their volumes.

The volume of spherical ballon being inflated changes at a constant rate.If initially its radius is 3 units and after 3 seconds it ios 6 units.Find the radius of the ballon after t second.