Q48 of 56 Page 13

Water is flowing at the rate of 2.52 km / h through a cylindrical pipe into a cylindrical tank, the radius of the base is 40 cm. If the increase in the level of water in the tank, in half and hour is 3.15 m, find the internal diameter of the pipe. (CBSE 2015)

Speed of water = 2.52kmph = 2520 m/hr


Length, h’ = 2520 m


Let the radius of the pipe be r’ and radius of the tank, r’’ = 40 cm = 0.4 m


Level of water in tank in half and hour = 3.15 m


Level of water in tank in an hour, h’’ = 6.30 m


Now, volume of pipe = volume of tank


⇒ π r’2 h’ = π r’’2 h’’


⇒ r’2 (2520) = (0.4)2 (6.3)



∴ diameter = 2r’ = 2 × 2 = 4 cm

More from this chapter

All 56 →
46

A farmer runs a pipe of internal diameter 20 cm from the canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km / h, in how much time will the tank be filled? (CBSE 2014)

 47

Sushant has a vessel of the form of an inverted cone, open at the top of height 11 cm and radius of top as 2.5 cm and is full of water. Metallic spherical balls each of diameter 0.5 cm are put in the vessel due to which of the water in the vessel flows out. Find how many balls were put in the vessel. Sushant made the arrangement so that the water that flows out irrigates the flower beds. What value has been shown by Sushant? (CBSE 2014)

 49

A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is . Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of ` 10 per cm2. (CBSE 2015)

 50

In Fig. 16.74, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid. (CBSE 2015)