### Cylinder

1. A hole is made in a solid cylinder of radius 10 cm and length 1000 cm to obtain a cylindrical shell (hollow cylinder) of uniform thickness and having an internal volume equal to one-fourth of the volume of the original solid cylinder. The thickness of the shell is....
a) 5 (√5 - 2) cm          b) 5 (2 - √3) cm             c) 5 cm             d) 5√2 cm
Sol: Let r be the radius of the hole.
∴ Thickness t + r = 10
⇒ r = 10 - t
Internal volume V1 = πr2 (1000) = 1000π (10 - t)2
Volume of solid cylinder V = π(10)2 (1000) = 1000π(10)2 Ans: c

2. A copper wire of diameter 3 mm is evenly and tightly wrapped on the cylinder of length 42 cm and diameter 49 cm to cover the whole surface. The adjacent coils touches each other. The length of the wire (approximately) will be.....
a) 215.6 m          b) 192 m          c) 205 m            d) 196.5 m
Sol: Number of turns Length of total wire = 154 × 140 cm = 215.6 m
Ans:a

3. A metal pipe of negligible thickness has radius 21 cm and length 90 cm. The outer curved surface area of the pipe (in cm2) is
a) 11880           b) 11680          c) 11480           d) 10080
Sol: Area of curved surface = 2πrh
= 2 × π × 21 × 90 (π = 22/7)
= 11880 cm2.
Ans: a

4. Some marbles each of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
a) 50          b) 150           c) 250           d) 350
Sol: Volume of each marble Total number of marbles = 150
Ans: b

5. Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and depth 2 m. In how much time will the cistern be filled?
a) 1 hr          b) 1 hr 40 mins         c) 1 hr 20 mins           d) 2 hrs 40 mins
Sol: Volume of water through circular pipe Ans: b

Posted Date : 24-04-2021