CLASS-VIII
SUB-MATHEMATICS
MENSURATION(SURFACE AREA AND VOLUME)
Worksheet-1(Basic)
I)
Multiple choice questions: (1 mark)
1.
The volume of a cube of side 0.03m is
a) 0.27 m
3
b) 0.027 m
3
c) 27 m
3
d) 2.7 m
3
2.
If the heights of a cylinder is halved, its volume will be of its
original volume
a)
1
times b)
2
1
times c) 2 times d) 3 times
3
3.
The lateral surface area of a cuboid whose length, breadth and height are 2a, 2b
and 2c respectively is.
a)
2(ab+bc+ca) b) 4(ab+bc+ca)
c) 8(a+b)c d) none of these
4.
The sum of the areas of all faces (excluding top and bottom) of a cuboid is the
_ of the cuboid.
a)
volume b)lateral surface area
c) total surface area d)none of these
5.
The volume of a cuboid whose length, breadth and height are 2a, 3a and 4a is.
a)24a
2
b)24a
3
c)12a
3
d)none of these
6.
The curved surface area of a right circular cylinder of radius 2r and height 2h is
a)2Πrh b)4Πrh c)8Πrh d)none of these
7.
The lateral surface area of a right circular cylinder of radius 3cm is 94.2cm
2
.The
height of the cylinder is
a)
5cm b)4.5cm c)5.5cm d)none of these
8.
If each edge of a cube is doubled, how many times will its volume increase?
a)2 times b)4 times c)8 times d)none of these
9.
If the volume of a cube is v, then the side(in terms of v)
a)v
3
b)
√
c)
3
√
d)v
2
10.
The volume of a cylinder whose diameter is equal to its height is
a)
Πr
3
h b)
3
8
c)

3
8
d)none of these
II)
Short answer questions type I (2 mark)
11.
Find the height of a cuboid whose volume is 756cm
3
and base area is 63cm
2
?
12.
The dimensions of a cuboid are in the ratio of 2:3:4 and its total surface area
is 280m
2
. Find the dimensions.
13.
If the volume of a cube
14.
The
circumference of the base of a right circular
cylinder is 2m,
find the curved surface area of the
15.
A roller of diameter
70cm
the area covered by the roller in 50
III)
Short answer questions
16.
A match box is
of dimension 4cm by 2.5cm by 1.5cm.What will be the
volume of a packet containing 12 such match boxes? How many such
can be placed in card board box whose size
17.
resulting cuboid.
18.
How many 8cm cubes can be cut out from the cube whose edge
19.
The
radius and height of a cylinder are in the ratio 5:7 and the volume
550 cm
3
.Find its total surface
20.
A rectangular sheet of paper 88cm x 10cm is rolled along its length and
cylinder is
formed. Find the volume of the
IV)
Long answer
questions
21.
The students of DAV were asked to participate in a competition
and decorating penholders in the shape of a cylinder with the base, using
cardboard. Each penholder was to be of radius 3cm and height 10.5cm.The
school was to supply the competitors with cardboard. If there were 35
competitors, how much cardboard w
competition?
22.
A cuboid is
of dimensions 60cm x 54cm x 30cm.How many small cubes of
side 6cm can be placed in the given
23.
The area of the base of a right circular cylinder
is 92400 cm
3.
Find
the area of the curved
24.
A cube of side 5cm
is
volume after such
cutting.
25.
The bottom of a tank measures 50m x 40m.Find its depth if
4000m
3
of water.
26.
A closed cylindrical tank
metal. How much sheet of metal
27.
A suitcase with measures 80cm x 48cm x 24cm
tarpaulin cloth. How many meters of tarpaulin of width
cover 100 such
suitcase.
28.
The lateral surface area of a hollow cylinder
height and formed a rectangular sheet of width 30cm.Find the perimeter of
rectangular sheet.
29.
A swimming pool
is
the cost of cem
enting its four walls and floor at the rate of 10 per
30.
Two cylinders of same volume have their radii in the ratio 1:6.Find the ratio
of their heights.
If the volume of a cube
is 512cm
3
.Find the total surface area of the
circumference of the base of a right circular
is
220cm. If the height of the
find the curved surface area of the
cylinder.
70cm
and the length 2m is
rolling on the ground .What
the area covered by the roller in 50
revolutions?
Short answer questions
type II (3 mark)
of dimension 4cm by 2.5cm by 1.5cm.What will be the
volume of a packet containing 12 such match boxes? How many such
can be placed in card board box whose size
is 60cm x 20cm x
24cm.
Two cubes, each of side 6cm, are joined end
to end. Find the volume of the
How many 8cm cubes can be cut out from the cube whose edge
radius and height of a cylinder are in the ratio 5:7 and the volume
.Find its total surface
area.
A rectangular sheet of paper 88cm x 10cm is rolled along its length and
formed. Find the volume of the
cylinder.
questions
(4 mark)
The students of DAV were asked to participate in a competition
and decorating penholders in the shape of a cylinder with the base, using
cardboard. Each penholder was to be of radius 3cm and height 10.5cm.The
school was to supply the competitors with cardboard. If there were 35
competitors, how much cardboard w
as required to be bought
for
of dimensions 60cm x 54cm x 30cm.How many small cubes of
side 6cm can be placed in the given
cuboid.
The area of the base of a right circular cylinder
is 15400 cm
2
and its volume
the area of the curved
surface.
is
cut into 1 cm
cubes. Find the percentage increase in
cutting.
The bottom of a tank measures 50m x 40m.Find its depth if
it
contains
A closed cylindrical tank
of radius 7m and height 3m is
made from a sheet of
metal. How much sheet of metal
is required?
A suitcase with measures 80cm x 48cm x 24cm
is
to be covered with a
tarpaulin cloth. How many meters of tarpaulin of width
96cm
suitcase.
The lateral surface area of a hollow cylinder
is 6600m
2
.It
is
height and formed a rectangular sheet of width 30cm.Find the perimeter of
is
40m in length, 20m in breadth and 5m in depth. Find
enting its four walls and floor at the rate of 10 per
Two cylinders of same volume have their radii in the ratio 1:6.Find the ratio
.Find the total surface area of the
cube
220cm. If the height of the
rolling on the ground .What
is
of dimension 4cm by 2.5cm by 1.5cm.What will be the
volume of a packet containing 12 such match boxes? How many such
packets
24cm.
to end. Find the volume of the
How many 8cm cubes can be cut out from the cube whose edge
is 32cm?
radius and height of a cylinder are in the ratio 5:7 and the volume
is
A rectangular sheet of paper 88cm x 10cm is rolled along its length and
a
The students of DAV were asked to participate in a competition
for making
and decorating penholders in the shape of a cylinder with the base, using
cardboard. Each penholder was to be of radius 3cm and height 10.5cm.The
school was to supply the competitors with cardboard. If there were 35
for
the
of dimensions 60cm x 54cm x 30cm.How many small cubes of
and its volume
cubes. Find the percentage increase in
contains
made from a sheet of
to be covered with a
96cm
is required to
is
cut along its
height and formed a rectangular sheet of width 30cm.Find the perimeter of
40m in length, 20m in breadth and 5m in depth. Find
enting its four walls and floor at the rate of 10 per
m
2
.
Two cylinders of same volume have their radii in the ratio 1:6.Find the ratio
CLASS-VIII
SUB-MATHEMATICS
MENSURATION(SURFACE AREA AND VOLUME)
Worksheet-2(Standard)
I)
Multiple choice questions (1 mark)
1.
A cuboid is 40cm x 20cm x 10cm.What would be the side of a cube having
the same volume?
a)
20cm b)40cm c)10cm d)30cm
2.
If each side of a cube is doubled then its volume
a)
is doubled b)becomes 4 times
c) becomes 6 times d)becomes 8 times
3.
The curved surface area of a cylindrical pillar is 264m
2
and its volume is
924m
3
.The ratio of its diameter to its height is.
a) 3:7 b)7:3 c)6:7 d)7:6
4.
A square sheet of paper is converted into cylinder by rolling it along its
length. What will be the ratio of the base radius to the side of a square?
a)1:2Π b) 2Π:1 c)1:1 d)1: Π
5.
If the radius of a right circular cylinder is decreased by 50% and its height is
increased by 60%, its volume will be decreased by
a)10% b)60% c)40% d)20%
II)
Short answer questions type I (2 mark)
6.
A birthday cake has two tiers as shown in the figure below. Find the
volume of the cake.
7.
A solid cube with an edge 10 cm is melted to form two equal cubes. Find
the ratio of the edge of the smaller cube to the edge of the bigger cube.
8.
Two cubes have their volumes in the ratio 8:27. Find the ratio of their
surface area.
9.
If the capacity of a cylindrical tank is 1848m
3
and the diameter of its base
is 14m.Find the depth of the tank.
10.
A school provides milk to the students daily in a cylindrical glasses of
diameter 7cm.If the glass is filled with milk up to height of 12cm,find how
many litres of milk is needed to serve 1600 students.
III)
Short answer questions type II (3 mark)
11.
A cuboid has a volume of 3000cm
3
, with height 15cm and length 20cm.
Find the area of the upper surface
12.
An iron cube has each side equal to 5cm.Find its volume and also its
weight in Kg if 1 cu.cm of iron weighs 50 grams.
13.
The sum of length, breadth and depth of a cuboid is 19cm and the diagonal
is 5√5.Find its surface area.
14.
A lateral surface area of a hollow cylinder is 4224 cm
2
it is cut along its
height and formed a rectangular sheet of width 32cm.Find the perimeter of
the rectangular sheet.
15.
A boy is cycling such that the wheels of the cycle are making 140
revolutions per hour.If the diameter of the wheel is 60cm,then calculate the
speed (in km/hr) with which the boy is cycling.
IV)
Long answer type questions ( 4 mark)
16.
Eight identical cuboidal wooden blocks are stacked one on top of the other.
The total volume of the solid formed is 128cm
3
if the height of each block
is 1cm and the base is a square .Find the dimension of each block.
17.
A metallic sheet is of rectangular shape with dimensions 48m x 36m. From
each of its corner, a square is cut off to make an open box. The length of
the square is 8m.Find the volume of the box.
18.
A hollow iron pipe is 21cm long and its external diameter is 8cm.If the
thickness of the pipe is 1cm and iron weighs 8g/cm
3
, find the weight of the
pipe.
19.
The ratio of radii of two cylinders is 1:2 and the heights are in the ratio 2:3.
Find the ratio of their volumes.
20.
Four times the area of a curved surface area of a cylinder is equal to the six
times the sum of the area of its base. If the height is 12cm , find its curved
surface area.
CLASS-VIII
SUB-MATHEMATICS
MENSURATION(SURFACE AREA AND VOLUME)
Worksheet-3(Advance)
1.
How many bricks of size 22cm x 10 cm x 7 cm are required to construct a
wall 11m long , 3.5 m high and 40 cm thick, if the cement and sand used in
the construction occupy
1
th part of the wall.
10
2.
The area of a side of a box is 120sq cm. The area of the other side of the box
is 72 sq cm. If the area of the upper surface of the box is 60sq cm then find the
volume of the box.
3.
A cylindrical tank has a radius of 154cm.It is filled with water to a height of
3m.If water to a height of 4.5m is poured into it, what will be the increase in
the volume of water in kilo litres.
4.
A rectangular examination hall having seats for 500 candidates has to be built
so, as to allow 4 cubic meters of air and 0.5 square meters of floor area per
candidate. If the length of the hall is 25m.Find the height and breadth of the
hall.
5.
In the given figure R is the radius of the base of the hat. Find the total outer
surface area of the hat.
6.
A hollow garden roller of 42cm diameter and length 152cm is
made of cast iron 2cm thick. Find the volume of iron used in the roller.
7.
A rectangular tank is 225m by 162m at the base. With what speed must the
water flow into it through an aperture 60cm by 45cm that the level may be
raised 20cm in 5 hours.
8.
A well with 20m diameter is dug 28m deep. Earth taken out of it spread all
around to a width of 10m to form an embankment. Find the height of
embankment.
9.
A wooden box including the lid has external dimensions 40cm x 34cm x
30cm.If the wood is 1cm thick, how many cm
3
of wood is used in it.
10.
Three cubes with sides in the ratio 3:4:5 are melted to form a single cube
whose diagonal is 12
√
3 cm. Find the sides of the cube.