Koushik got a playing top as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm. in height and the diameter of the top is 3.5 cm. Find the area he has to colour. (Take `pi=22/7`)

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of right circular cone mounted on a hemisphere is immersed into the tub. The radius of the hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm. Find the volume of water left in the tub. " "("Take "pi=22/7)

A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in the adjacent figure. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical position has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion is to be painted yellow, find the area of the rocket painted with each of these colour. (Take pi = 3.14)

Parvali house has a water tank in the shape of a cylinder on the roof. This is filled by pumping water from a sump (an underground tank) which is in the shape of a cuboid. The sump has dimensions 1.57 m times 1.44 m times 9.5 cm. The water tank has radius 60 cm. and height 95 cm. Find the height of the water left in the sump after the water tank has been completely filled with water from the sump which had been full of water. Compare the capacity of the tank with that of the sump. ( pi =3.14)

A 1.5 m tall boy is looking at the top of a temple which is 30 m in height from a poin at certain distance. The angle of elevation from his eye to the top of the crown of the temple increases from 30^(@)" to "60^(@) as he walks towards the temple. Find the distance he walked towards the temple.

A vessel is in the form of an inverted cone. Its height is 8 cm. and the radius of its top is 5 cm.It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, 1/4 of the water flows out. Find the number of lead shots dropped into the vessel.

A juice seller was serving his customers using glasses as shown in the adjacent figure. The inner diameter of the cylinderical glass was 5 cm, but the bottom of the glass had a hemi-spherical raised portion which reduced the capacity of the glass. If the height of the glass was 10 cm, find the apparent capacity of the glass and its actual capacity. (use pi = 3.14)