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21. The diameter of a cylinder tank is 24.5 metres and depth 32 metres.How many metric tons of water will it hold?
  A.   15098 metric tonnes
  B.  15088 metric tonnes
  C.  15092 metric tonnes
  D.  15095 metric tonnes
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then volume of the cylinder is given by (πr2h) cubic units.
or Vol. of cylinder = Area of the base of cylinder x Height of the cylinder.
Here, h = 32,
r =
24.5 / 2

Vol. of cylinder = π(r)2 x h
=
22 / 7
x
245 x 245 / 20 x 20
x 32
= 22 x 49 x 7 x 2 = 15092
Hence,the volume of cylinder is 15092 cubic m.
Since 1 cubic metre = 1 metric ton [∵ 1000kg = 1 metric ton]
∴ cylinder will hold 15092 metric tonnes.

22. Find how many pieces of money
3 / 4
cm in diamter and
1 / 8
cm thick must be melted down to form a cube whose edge is 3 cm long?
  A.  491
  B.  481
  C.  485
  D.  489
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then volume of the cylinder is given by (πr2h) cubic units.
or Vol. of cylinder = Area of the base of cylinder x Height of the cylinder.
Here, h =
1 / 8

r =
3 / 8

Vol. of cylinder = π(r)2 x h
=
22 / 7
x
3 x 3 / 8 x 8
x
1 / 8

=
22 x 3 x 3 x 1 / 7 x 8 x 8 x 8
= 488.72 ≈ 489
Hence, 489 pieces can be melted down.

23. The area of curvec surface of a cylinder is 4400 cm2 and the circumference of its base is 110 cm.Find the height and the volume of the cylinder.
  A.  height: 40cm;circumference: 38500 cu cm.
  B.  height: 30cm;circumference: 38800 cu cm.
  C.  height: 45cm;circumference: 37200 cu cm.
  D.  height:38cm;circumference: 38200 cu cm.
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then volume of the cylinder is given by (πr2h) cubic units.
or Vol. of cylinder = Area of the base of cylinder x Height of the cylinder.
Here, h =
4400 / 110
= 40
Circumference = 110
or, 2πr = 110
r =
55 / 22/7
=
5 x 7 / 2
=
35 / 2

Vol. of cylinder = π(r)2 x h
=
22 / 7
x
35 x 35 / 2 x 2
x 40
=
22 x 35 x 35 x 40 / 7 x 2 x 2
= 22 x 5 x 35 x 10 = 38500
Hence, the volume of cylinder is 38500 cubic cm.

24. How many cubic metres of the earth must be dug out to sink a well 21 metres deep and 6 metres in diameter? Find the cost of plastering the inner surface of the well at Rs 9.50 per sq. metre.
  A.  592 cu m; Rs 4762
  B.  594 cu m; Rs 3762
  C.  596 cu m; Rs 4762
  D.  591 cu m; Rs 3862
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then curved surfce area of the cyinder is 2πrh sq units.
or Surface Area = Circumference of the base x height
Here, r =
6 / 2
= 3, h = 21
Volume of the earth dug out = Volume of the well
=
22 / 7
x 3 x 3 x 21 = 594 cubic m
Curved S.A of the well = 2πrh
= 2 x
22 / 7
x 3 x 21 = 396
The S.A of the well is 396 sq m.
∴ Required cost = 396 x 9.50 = Rs 3762

25. A cylinderical tower is 5m in diameter and 14 m high.The cost of white washing its curved surface at 50 paisa per sq meter is.
  A.  Rs 115
  B.  Rs 120
  C.  Rs 105
  D.  Rs 110
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then curved surfce area of the cyinder is 2πrh sq units.
or Surface Area = Circumference of the base x height
Here, h = 14
r =
5 / 2

Curved S.A of the well = 2πrh
= 2 x
22 / 7
x
5 / 2
x 14
= 2 x 22 x 5 = 220
The S.A of the well is 220 sq m.
∴ Required cost = 220 x 0.50 = Rs 110

26. The height of a cylinder is 14 cm and its curved surface is 264 cm 2. The radius of its base is :
  A.  3 cm
  B.  1 cm
  C.  5 cm
  D.  4 cm
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then curved surfce area of the cyinder is 2πrh sq units.
or Surface Area = Circumference of the base x height
Here, h = 14
S.A = 264

Curved S.A of the well = 2πrh
264 = 2 x
22 / 7
x r x 14
r =
264 x 7 / 2 x 22 x 14
= 3
∴ Radius is 3 cm.

27. Find the total surface area of a cylinder of length 80 cm and the diameter of whose base is 7 cm.
  A.  1835 sq cm
  B.  1839 sq cm
  C.  1837 sq cm
  D.  1832 sq cm
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then the total surface area of the cylinder is 2πrh + 2πr2 sq units.
or Total Surface Area = 2πr(h + r) sq units or Circumference x (height + radius)
Here, h = 80, r =
7 / 2
= 3.5
Using these values in the shortcut, we get:
Total S.A = 2πrh + 2πr2
= (2 x
22 / 7
x 3.5 x 80) + (2 x
22 / 7
x 3.5 x 3.5)
= (2 x 22 x 0.5 x 80) + (2 x 22 x 0.5 x 3.5)
= 1760 + 77 = 1837
Hence, total surface area of a cylinder is 1837 sq cm.

28. A solid cylinder has a total surface area of 231 square cm. Its curved surface area is
2 / 3
of the total surface area. Find the volume of the cylinder.
  A.  270.5 cu cm
  B.  269.5 cu cm
  C.  265.25 cu cm
  D.  268.5 cu cm
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then the total surface area of the cylinder is 2πrh + 2πr2 sq units.
or Total Surface Area = 2πr(h + r) sq units or Circumference x (height + radius)
Here, Total S.A = 231,
Curved S.A =
2 / 3
x Total S.A
2πrh =
2 / 3
x 231
2πrh = 154
Total S.A = 2πrh + 2πr2
231 = 154 + 2πr2
231 − 154 = 2πr2
77 = 2πr2
r2 =
77 / 2π
=
77 / 2 x 22/7
=
77 x 7 / 2 x 22
=
7 x 7 / 2 x 2

r =
√(
7 x 7 / 2 x 2
)
=
7 / 2

We know that 2πrh = 154
so, 2 x
22 / 7
x
7 / 2
x h = 154
2 x 11 x h = 154
∴ h = 7
Now, volume = 2πr2h
= 2 x
22 / 7
x
7 x 7 / 2 x 2
x 7 = 269.5
Hence, the volume of the cylinder is 269.5 cubic cm.

29. The sum of the radius of the base and the height of a solid cylinder is 37 m. If the total surface area of the cylinder be 1628 sq m, find the volume.
  A.  4650 cu cm
  B.  4580 cu cm
  C.  4640 cu cm
  D.  4620 cu cm
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then the total surface area of the cylinder is 2πrh + 2πr2 sq units.
or Total Surface Area = 2πr(h + r) sq units or Circumference x (height + radius)
Here, r + h = 37 and 2πr(h + r) = 1628
so, πr =
1628 / 74
= 22
∴ r = 7 cm and h = 37 − 7 = 30 cm
∴ Vol. = πr2h
=
22 / 7
x 7 x 7 x 30 = 4620
Hence, the volume is 4620 cubic cm.

30. The ratio of total surface area to lateral surface area of a cylinder whose radius is 80 cm and height is 20 cm is:
  A.  3 : 4
  B.  2 : 3
  C.  5 : 1
  D.  5 : 3
     
   
View Answer

Shortcut:
If the radius of the base of a cylinder is 'r' units and its height (or length) is 'h' units, then the total surface area of the cylinder is 2πrh + 2πr2 sq units.
or Total Surface Area = 2πr(h + r) sq units or Circumference x (height + radius)
Here,
Total S.A / Lateral S.A
=
2πr(h + r) / 2πrh
=
(h + r) / h

h = 20, r = 80
so,
(20 + 80) / 20
=
5 / 1
or 5 : 1
Hence,
Total S.A / Lateral S.A
= 5 : 1

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