Chapter 11: Mensuration

Example 1 :What is the area of the triangle ADE in the following figure?
BCDA8 cm10 cmE
(a)45 cm2(b)50 cm2(c)55 cm2(d)40 cm2
Solution:The correct answer is (d).
Example 2:What will be the change in the volume of a cube when its side becomes 10 times the original side?
(a)Volume becomes 1000 times.
(b)Volume becomes 10 times.
(c)Volume becomes 100 times.
(d)Volume becomes 1/1000 times.
Solution:The correct answer is (a).

1.A cube of side 5 cm is painted on all its faces. If it is sliced into 1 cubic centimetre cubes, how many 1 cubic centimetre cubes will have exactly one of their faces painted?
(a)27(b)42(c)54(d)142

2.A cube of side 4 cm is cut into 1 cm cubes. What is the ratio of the
surface areas of the original cubes and cut-out cubes?
(a)1 : 2(b)1 : 3(c)1 : 4(d)1 : 6
3.A circle of maximum possible size is cut from a square sheet of board.
Subsequently, a square of maximum possible size is cut from the
resultant circle. What will be the area of the final square?
(a)3
4 of original square.(b)1
2 of original square.
(c)1
4 of original square.(d)2
3 of original square.
4.What is the area of the largest triangle that can be fitted into a
rectangle of length l units and width w units?
(a)lw/2(b)lw/3(c)lw/6(d)lw/4
5.If the height of a cylinder becomes 1
4 of the original height and the
radius is doubled, then which of the following will be true?
(a)Volume of the cylinder will be doubled.
(b)Volume of the cylinder will remain unchanged.
(c)Volume of the cylinder will be halved.
(d)Volume of the cylinder will be 1/4of the original volume.

6.If the height of a cylinder becomes 1
4 of the original height and the
radius is doubled, then which of the following will be true?
(a)Curved surface area of the cylinder will be doubled.
(b)Curved surface area of the cylinder will remain unchanged.
(c)Curved surface area of the cylinder will be halved.
(d)Curved surface area will be 1
4 of the original curved surface.
7.If the height of a cylinder becomes 1
4 of the original height and the
radius is doubled, then which of the following will be true?
(a)Total surface area of the cylinder will be doubled.
(b)Total surface area of the cylinder will remain unchanged.
(c)Total surface of the cylinder will be halved.
(d)None of the above.
8.The surface area of the three coterminus faces of a cuboid are 6, 15
and 10 cm2 respectively. The volume of the cuboid is
(a)30 cm3(b) 40 cm3 (c) 20 cm3(d) 35 cm3

9.A regular hexagon is inscribed in a circle of radius r. The perimeter
of the regular hexagon is
(a)3r(b) 6r(c) 9r(d)12r
10.The dimensions of a godown are 40 m, 25 m and 10 m. If it is filled
with cuboidal boxes each of dimensions 2 m × 1.25 m × 1 m, then
the number of boxes will be
(a)1800(b)2000(c)4000(d)8000

11.The volume of a cube is 64 cm3. Its surface area is
(a)16 cm2(b)64 cm2(c)96 cm2(d)128 cm2
12.If the radius of a cylinder is tripled but its curved surface area is
unchanged, then its height will be
(a)tripled(b)constant(c)one sixth(d)one third
13.How many small cubes with edge of 20 cm each can be just
accommodated in a cubical box of 2 m edge?
(a)10(b)100(c)1000(d)10000
14.The volume of a cylinder whose radius r is equal to its height is
(a)1
4πr3(b)
πr3
32(c)πr3(d)
3
8
r
15.The volume of a cube whose edge is 3x is
(a)27x3(b)9x3(c)6x3(d)3x3

16.The figure ABCD is a quadrilateral in which AB = CD and
BC = AD. Its area is
(a)72 cm2(b)36 cm2(c)24 cm2(d)18 cm2
17.What is the area of the rhombus ABCD below if AC = 6 cm, and
BE = 4cm?
(a)36 cm2(b)16 cm2(c)24 cm2(d)13 cm2

18.The area of a parallelogram is 60 cm2 and one of its altitude is 5 cm.
The length of its corresponding side is
(a)12 cm(b)6 cm(c)4 cm(d)2 cm
19.The perimeter of a trapezium is 52 cm and its each non-parallel side
is equal to 10 cm with its height 8 cm. Its area is
(a)124 cm2(b)118 cm2(c)128 cm2(d)112 cm2
20.Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD
from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a)4 cm(b)15 cm(c)16 cm(d)18 cm
21.A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into
a cube. The side of the cube is
(a)6 cm(b)8 cm(c)12 cm(d)24 cm
22.Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm
respectively are melted to form a single cube. The edge of the new
cube is
(a)12 cm(b)24 cm(c)18 cm(d)20 cm
23.A covered wooden box has the inner measures as 115 cm, 75 cm and
35 cm and thickness of wood as 2.5 cm. The volume of the wood is
(a)85,000 cm3(b)80,000 cm3 (c)82,125 cm3(d)84,000 cm3
24.The ratio of radii of two cylinders is 1: 2 and heights are in the ratio
2:3. The ratio of their volumes is
(a)1:6(b)1:9(c)1:3(d)2:9

25.Two cubes have volumes in the ratio 1:64. The ratio of the area of a
face of first cube to that of the other is
(a)1:4(b)1:8(c)1:16(d)1:32
26.The surface areas of the six faces of a rectangular solid are 16, 16,
32, 32, 72 and 72 square centimetres. The volume of the solid, in
cubic centimetres, is
(a)192(b)384(c)480(d)2592
27.Ramesh has three containers.
(a)Cylindrical container A having radius r and height h,
(b)Cylindrical container B having radius 2r and height 1/2 h, and
(c)Cuboidal container C having dimensions r × r × h
The arrangement of the containers in the increasing order of their
volumes is
(a) A, B, C

(b) B, C, A
(c) C, A, B

(d) cannot be arranged
28.If R is the radius of the base of the hat, then the
total outer surface area of the hat is
(a)πr (2h + R)(b) 2πr (h + R)
(c) 2 πrh + πR2(d) None of these
In questions 29 to 52, fill in the blanks to make the statements true.
29.A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cubic
cm cubes, then number of such cubes that will have exactly two of
their faces painted is __________.
30.A cube of side 5 cm is cut into 1 cm cubes. The percentage increase
in volume after such cutting is __________.
31.The surface area of a cuboid formed by joining two cubes of side a
face to face is __________.

32.If the diagonals of a rhombus get doubled, then the area of the
rhombus becomes __________ its original area.
33.If a cube fits exactly in a cylinder with height h, then the volume of
the cube is __________ and surface area of the cube is __________.
34.The volume of a cylinder becomes __________ the original volume if
its radius becomes half of the original radius.
35.The curved surface area of a cylinder is reduced by ____________
per cent if the height is half of the original height.
36.The volume of a cylinder which exactly fits in a cube of side a is
__________.
37.The surface area of a cylinder which exactly fits in a cube of side b is
__________.
38.If the diagonal d of a quadrilateral is doubled and the heights h1 and
h2 falling on d are halved, then the area of quadrilateral is __________.
39.The perimeter of a rectangle becomes __________ times its original
perimeter, if its length and breadth are doubled.

40.A trapezium with 3 equal sides and one side double the equal side
can be divided into __________ equilateral triangles of _______ area.
41.All six faces of a cuboid are __________ in shape and of ______ area.
42.Opposite faces of a cuboid are _________ in area.
43.Curved surface area of a cylinder of radius h and height r is _______.
44.Total surface area of a cylinder of radius h and height r is _________
45.Volume of a cylinder with radius h and height r is __________.

46.Area of a rhombus = 1
2 product of _________.
47.Two cylinders A and B are formed by folding a rectangular sheet of
dimensions 20 cm × 10 cm along its length and also along its breadth
respectively. Then volume of A is ________ of volume of B.
48.In the above question, curved surface area of A is ________ curved
surface area of B.
49.__________ of a solid is the measurement of the space occupied by it.
50.__________ surface area of room = area of 4 walls.
51.Two cylinders of equal volume have heights in the ratio 1:9. The
ratio of their radii is __________.
52.Two cylinders of same volume have their radii in the ratio 1:6, then
ratio of their heights is __________.