Sheet MENSURATION – 3D
08
– 3D
27. Find the length of wire of radius 0.25 cm which 2 1 1 1
can completely cover the surface of a cylinder (a) 2 (b) 1 (c) 2 (d) 1
3 2 4 3
whose height is 1.2 m and base radius 14 cm.
Hollow Cylinder
1. The volume of the metal of a cylindrical pipe is
748 cm³. The length of the pipe is 14 cm and its
(a) 21232 cm (b) 21120 cm external radius is 9 cm. Its thickness is:/
(c) 20122 cm (d) 22012 cm 3
28. A right circular cylinder of radius 9 cm and height
16 cm, is cut into four equal parts by 3 cuts par-
allel to base. What is % increase in total surface (a) 1 cm (b) 1.25 cm
area ? (c) 0.75 cm (d) 1.5 cm
2. A hollow iron pipe is 21 cm long and its exterior
diameter is 8 cm. If the thickness of the pipe is 1
cm and iron weights 8 gm/cm³, then the weight of
22
(a) 72% (b) 96% (c) 144% (d) 108% the pipe is. (take π =
7
29. A right circular cylinder of radius 7 cm and height cm
21 cm, is cut into four parts. One cut is made par- cm 1 cm gm/
allel to the base of cylinder and another cut along
the axis of cylinder from top to bottom base. What cm³
is % increase in total surface area of cylinder?
(a) 3.696 kg (b) 3.6 kg
(c) 36 kg (d) 36.9 kg
3. A hollow cylinder of thickness 0.7 cm and height
15cm is made of Iron. If internal radius is 3.5 cm
then what is the total surface area (in cm²) of hol-
low cylinder?
(a) 75% (b) 81.81%
(c) 72.72% (d) 77.77%
30. Water is flowing at a speed of 1.25 m/sec through
a pipe of diameter of 0.14 m into a rectangular (a) 812.12 cm² (b) 768.42 cm²
tank, which is 60 m long and 44 m wide. What is
(c) 759.88 cm² (d) 828.42 cm²
the time (in hours) in which the water level in the
4. A hollow cylinder is made up of metal. The differ-
tank will rise by 7 cm ?
ence between outer and inner curved surface area
of this cylinder is 352 cm². Height of the cylinder
is 28 cm. If the total surface area of this hollow
cylinder is 2640 cm², then what are the inner and
outer radius (in cm)?/
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7. A well of radius ‘r’ is dug 20 m deep and the earth
2
taken out is spread all around it to a width of 1 m
to form an embankment. The height of the em-
bankment is 5 m then find the value of ‘r’ ?/
(a) 4, 6 (b) 10, 12 (c) 8, 10 (d) 6, 8 r
5. The external and the internal radii of a hollow right
circular cylinder of height 15 cm are 6.75 cm and
r
5.25 cm respectively. If it is melted to form a solid
cylinder of height half of the original cylinder, then
the radius of the solid cylinder is.
1+ 5 1+ 5
(a) (b)
2 4
5 –1 5 –1
(c) (d)
2 4
(a) 5 cm (b) 6 cm (c) 7 cm (d) 8 cm
6. A well with inner radius 3 m, is dug 6 m deep. The
soil taken out of it has been spread evenly all
around it to a width of 2 m to form an embank-
ment. The height (in m) of the embankment is:
1 1 1 3
(a) 4 (b) 4 (c) 3 (d) 3
2 4 4 8
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