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BOOK 8 ( CBSE ) / Chap 11 /Mensuration
Chapter Facts.
Let’s recall : 1. Perimeter of a rectangle = 2 × (length + breadth)
2. Area of a rectangle = length × breadth
3. Perimeter of a square = 4 × length of its side.
4. Area of square = side x side or side2.
5. Perimeter of triangle = sum of lengths of three sides.
6. Perimeter of an equilateral triangle = 3 × length of a side.
7. Area of a triangle = ½ × base × corresponding height
8. Perimeter of parallelogram = 2 x sum of lengths of adjacent sides.
9. Circumference of a circle =2
 r or  d : r is the radius of the circle ; where d is the
diameter of the circle and π = 22/7 or 3.14 (approximately).
10. A wheel covers a distance equal to its circumference in one rotation.
11. Hence distance covered by a wheel in ‘n’ rotations = n x circumference
Or n x 2  r.
12.Area of a circle =
 r 2, where r is the radius of the circle.
13. Area of annulus of a circle= π( R + r ) ( R – r ).
14. Area of a quadrilateral = ½ x ( diagonal ) x ( sum of offsets)
Note : - perpendiculars let fall from opposite vertices are called offsets.
area ABCD = ½ x AC x (BL + DM )
15. Area of a trapezium =
1
( base1  base2 ) corresponding height
2
Note : Parallel sides are called bases.
area trapz. ABCD =
1
( AB  DC ) h
2
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16. Number of tiles needed to cover a floor =
area of
floor
area of one tile
17. A polygon can be divided into triangles and trapeziums.
To find the area of the polygon we find area of each of these and add all of them.
18. Surface area of a solid is the sum of the areas of its faces.
19. If a solid is kept vertically then surface of its walls ( area excluding base and top ) is
called its lateral surface and the area of this surface is called lateral surface area. ( LSA)
Also area of all the surfaces taken together ( lateral surface , top and bottom ) is called
total surface area ( TSA ).
20. LSA of cube = 4 x side2.
21. TSA of cuboid = 6 x side2
22. LSA of cuboid = 2 ( L + B ) x H
23. TSA of cuboid = 2(LB + BH + HL)
24. LSA of cylinder = 2  rh
25. TSA of cylinder = 2
 r(r+h)
26. Area leveled by a cylindrical roller in ‘n’ revolutions = n x CSA or n x2  rh
27. Area can be converted from one unit to another using the following figure.
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.
28. Sometimes area is measured in ‘are’ . 1 are = 100 m2.
29. Amount of space occupied by a solid is called its volume.
The quantity of a fluid a container can hold is called its capacity.
30. Volume of a cuboid = L × B × H
31. Volume of a cube = side 3.
32. Volume of a cylinder =
 r2 h
33. Volume is measured in cm3 / ml ; dm3 or l ( liter ) ; m3 or kl ( kiloliter )
volume can be converted from one unit to other using the following figure.
..
Formative Assessment
A ) Multiple Choice Questions
Tick () the correct answer for each of the following :
1. The volume of a cube is 1728 cm2, Its lateral surface area is
(a) 864 m2
(b) 216 m2
(c) 576 m2
(d) 144 m2
2. The circumference of the base of a cylinder is 176 cm and its height is 40 cm. The
lateral surface area of cylinder is
(a) 7040 cm2
(b) 98560 cm2
(c) 11440 cm2
(d) 14080 cm2
3. If each edges of a cuboid , its volume will
(a) become half
(b) become one–fourth
eighth
(d) remain unchanged
(c)
become one–
4. The volume of a cube whose total surface area is 294 cm2 is
(a) 216 cm3
(b) 343 cm2
(c) 512 cm3
(d) 729 cm2
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5. A cardboard box is 1.5 m long, 84 cm wide and 60 cm high. The number of soap
bars measuring 6 cm × 4 cm × 3.5 cm that it can hold is
(a) 7500
(b) 8000
(c) 8500
(d) 9000
6. The height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2
is
(a) 20 cm
(b) 12 cm
(c) 15 cm
(d) 10 cm
7. The number of cubes of sides 8 cm that can be placed in the cuboid of dimensions
64 cm × 48 cm × 32 cm is
(a) 192
(b) 182
(c) 100
(d) 512
8. The length of a cuboid whose volume, height and breadth are respectively 288 m3,
12 m and 8 m is
(a) 6 m
(b) 4 m
(c) 5 m
(d) 3 cm
9. The capacity of a cylindrical tub whose base diameter is 16 cm and height is 3.5 cm
is
(a) 704 l
(b)0.704 l
(c) 70.4 l
(d) 7.04 l
10. The number of cuboidal boxes with volume of 0.8 m3 per box that can be stored in
the godown measuring 60 m × 40 m × 30 m is
(a) 90,000
(b) 9,000
(c) 45,000
(d) 30,000
11. The volume of a rectangular tank is 1596 m3. If its length and breadth are
respectively 12 m and 9.5 m, its depth is
(a) 14 m
(b) 13 m
(c) 12 m
(d) 11 m
12. A rectangular water tank is 2 m 50 cm by 1 m 60 cm by 1 m 40 cm. How many
liters of waters does it hold when filled to the brim?
(a) 5,600 l
(b) 560 l
(c) 5,60,000 l
(d) 56000 l
13. The side of a cube whose surface area is 726 cm2 is
(a) 13 cm
(b) 11 cm
(c) 15 cm
(d) 17 cm
14. The height of a cuboid whose volume is 756 cm3 and base area is 63 cm2 is
(a) 24 cm
(b) 12 cm
(c) 10 cm
(d) 6 cm
15. If each edge of a cube is doubled, its surface area will
(a) become double
(b) become four times
times
(d) remain unchanged
(c)
become eight
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B ) Fill in the blanks:
1. Perimeter of a rectangle = ___________________________
2. Area of a rectangle = ___________________________
3. Perimeter of a square = = ___________________________
4. Area of square = = ___________________________
5. Perimeter of triangle = ___________________________
6. Perimeter of an equilateral triangle = ___________________________ .
7. Area of a triangle = = ___________________________
8. Perimeter of parallelogram = ___________________________ .
9. Circumference of a circle = ___________________________
10. Hence distance covered by a wheel in ‘n’ rotations = _____________________
11.Area of a circle = ___________________________
12. Area of annulus of a circle= ___________________________
13. Area of a quadrilateral = ___________________________
14. Area of a trapezium = ___________________________
15. Number of tiles needed to cover a floor = ___________________________
16. LSA of cube = ___________________________
17. TSA of cuboid = ___________________________
18. LSA of cuboid = ___________________________
19. TSA of cuboid = ___________________________
20. LSA of cylinder = ___________________________
21. TSA of cylinder = ___________________________
22. Area leveled by a cylindrical roller in ‘n’ revolutions =
_______________________
23. Volume of a cuboid = ___________________________
24. Volume of a cube = ___________________________
25. Volume of a cylinder = ___________________________
C) True / False
Say true or false for each of the following.
1. The lateral surface area of a cube is 6a2.
T/F .
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2. If we join two cubes each of edge x, then the total surface area will be double of one
such cube.
T/F
4. If we double each edge of a cube, its surface area becomes four times.
T/F
5. If each dimension of a cuboid is halved, its volume also becomes half of the
original volume.
T/F
6. If we interchange the length of the base and the height of a cuboid to get another
cuboid, its LSA will change but TSA will remain same.
T/F
7. If we melt a cylinder to form a cube, then the volume of the two solids will be
same. T/F
8. The volume of a cylinder is obtained by multiplying the area of its base by the
height. T/F
9. To find the total cost of painting a solid object, we have to find its volume.
10.
T/F
The lateral surface area of a cylinder is equal to the product of area of its base and
height of a cylinder.
T/F
D ) True / False with Justification :
Say true or false for each of the following. Justify your answer ?
1. Lateral surface area of a solid is always more than total surface area . T/F .
________________________________________________________________
_________________________________________________________________
2. Two objects of same volume will have same surface area also.
T/F
________________________________________________________________
_________________________________________________________________
3. Interior of a vessel is a cube of side 10 cm . The capacity of the vessel is 1 liter. T/F .
________________________________________________________________
_________________________________________________________________
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E ) Matching
1. Match the items in column I with items in column II.
Column I
(i)
l, b and h of a cuboid is made two
Column II
A CSA becomes one–fourth.
(ii)
times
Edge ‘a’ of a cube is made three
B
Volume becomes three times
(iii)
times.
r of a cylinder remaining the same,
C
CSA becomes one–ninth.
(iv)
h becomes five times.
l and b of a cuboid remaining the
D
Volume becomes one–eighth.
E
F
Volume becomes 5 times
Surface area becomes four times
G
Surface area becomes nine-times.
same, h
(v)
(vi)
is trippled.
Edge ‘a’ of a cube halved.
r and h or a cylinder becomes one–
third.
Summative Assessment
A ) One mark questions
1. Find area of trapezium with parallel sides 10 cm and 12 am and altitude 8 cm.
2. Find the area of a quadrilateral with diagonal 10 m and offsets 8 m and 5 m.
3. Find the area of a rhombus with side 8 cm and corresponding altitude 7 cm .
4. Find area of a rhombus with diagonals 12 cm and 10 cm.
5. Find LSA of a cube with edge 12 cm.
6. Find TSA of a cube with edge 10 cm.
7. Find LSA of a cuboid with length 10 cm , breadth 8 cm and height 6 cm
8. Find TSA of a cuboid with length 9 cm , breadth 7 cm and height 4 cm
9. Find CSA of a cylinder with radius of base 7 cm and height 12 cm.
10. Find TSA of a cylinder with radius of base 5 cm and height 9 cm.
11.
What will happen to the volume of a cubiod, if each of its side is halved?
12.
Find the area of four walls of a room measuring 10 m x 5 m
 6 m (height).
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13.
Two cubes of edges 5 cm are joined end to end. What will be the lateral surface area
of
resulting cuboid?
14.
Find the volume of a cuboid whose length is 2 m, breadth is 75 cm, height 1 ½ m in
m3.
B ) Two mark questions
15. Find the height of a trapezium, the sum of lengths of whose bases is 80 cm and whose
area is 800 cm2.
16. Find the sum of the lengths of the bases of a trapezium whose altitude is 22 cm and
whose area is 550 cm2.
17. The area of a trapezium is 210 cm2 and its height is 14 cm. If one of the parallel sides
is longer than the other by 12 cm, find the two parallel sides.
18. Area of a trapezium is 144 cm2 and its height is 12 cm. If one of the parallel side is
two times the other, find the two parallel sides.
19. The volume of a cuboid is 70 cm3. and the area of the base is 10 sq. cm. Find the
height.
6. How many bricks of size 6 cm by 20 cm by 7 cm will be required to build a wall, 15 m
by ½ m by 7 m ?
20. Find the volume of a cube whose total surface area is 150 cm2.
21. A match box measures 5 cm
 3 cm  2 cm. What will be the volume of a packet
containing 12 such boxes.
22. A cuboidcal tank is built 60 cm x 40 cm
 30 cm. How many litres of water it can
hold?
23. Capacity of a tank is 5000 l. If its length is 5 m and breadth is 4 m find its depth in
cm.
24. Material measurement of a solid cuboidal box are 20 cm
 16 cm v 24 cm. How
many cubes of sides 4 cm can be put into the box?
25. If each side of a cube is doubled then find the percentage increase in its volume.
26. The radii of two right circular cylinders are in ratio 2 : 3 and their heights are in ratio
5 : 4. Calculate the ratio of their curved surfaces areas.
27. A cylinder whose height is 7/44 times of its diameter, has same volume as a cube of
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side 4 cm. Calculate the radius of base of the cylinder.
C ) Three mark questions
28. A room is 4.5 m long, 3 m wide and 2.8 m high. It has one door 1.4 m wide and 2 m
high and two rectangular windows 2 m
 1.5 m each. Find the cost of white washing the
inner four walls @ Rs. 100/m2.
29. A field is 200 m long and 150 m broad. There is a plot 50 m long and 40 m broad,
near the field. The plot is dug 7 m deep and the earth taken out is spread evenly on the
field. By how many
metres is the level of the field raised? Give answers to second place of decimal.
30. The inner diameter of a circular well is 35 m and it is 10 m deep. Find the cost of
plastering the inner surface @ Rs. 4 per sq. m.
31. A powder is available in two packs, a tin pack with a square baser of each side 5 cm
and having height 12 cm or one with a circular base of radius 3 : 5 cm and having height
10 cm. Which of them has greater capacity and by how much?
32. How many full bags of wheat can be emptied into a circular drum of radius 4.2 m and
height 3.5 m. If space required for one bag of wheat is 2.1 m3?
D ) Four mark questions
33. Three cubes of metal whose edges are 6 cm, 8 cm and 10 cm are melted and one new
cube is made. Find the total surface area of the new cube.
34. Area of adjacent faces of a cuboid are x, y and z. Show volume of cuboid is
xyz .
35. A garden roller is 20 cm in diameter and 77 cm in which. What area will be covered
in 100 revolutions ?
36. A cylindrical vessel open at the top has a diameter of 20 cm and height 14 cm. Find
the cost of plating on the inside @ Rs. 2.1 per 100 sq.m.
37. A cylinder is open at both ends and is made of metal 2 cm thick. Its external diameter
is 10 cm and height is 40 cm. Find the volume of metal used in making the cylinder and
weight of the cylinder, If 1 cm3 of metal weights 8 g. (Use

= 3.14)
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