Question Set D

CBSE 9th Standard Mathematics Surface Areas and Volumes Model Questions Papers Study Material - QB365

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Questions:

Multiple Choice Question

38 x 1 = 38

The area of the four walls of a room is 80 cm² and its height is 4 m. Then, the perimeter of the floor of the room is

(a)

16 m

(b)

5 m

(c)

20 m

(d)

10 m

The area of the four walls of a room is 300 m². Its length and height are 15 m and 6 m respectively. Find its breadth.

(a)

10 m

(b)

5 m

(c)

20 m

(d)

15 m

The dimensions of a box are 1 m, 80 cm and 50 cm. The area of its four walls is

(a)

6000 cm²

(b)

12000 cm²

(c)

18000 cm²

(d)

24000 cm²

A brick measures 25 cm \(\times\) 12 cm \(\times\) 10 cm. Its surface area is

(a)

670 cm²

(b)

1340 cm²

(c)

3000 cm²

(d)

1500 cm²

The side of a cube is 1 cm. The total surface area of the figure formed by joining two such cubes is

(a)

2(2 + 1 + 2) cm²

(b)

2(2 + 2 + 2) cm²

(c)

2(1 + 1 + 1) cm²

(d)

2(1 + 1 + 2) cm²

The lateral surface area of a cuboid of length l, breadth b and height h is

(a)

2(lb + bh + hl)

(b)

2(l + b)h

(c)

lbh

(d)

none of these.

If the edges of a cuboid are l, b and h respectively, then the total surface area of the cuboid is

(a)

2(lb + bh + hl)

(b)

lbh

(c)

2(l + b)h

(d)

none of these.

The lateral surface area of a cube of side a is

(a)

4a²

(b)

6a²

(c)

3a²

(d)

2a².

The total surface area of a cube of side a is

(a)

4a²

(b)

6a²

(c)

3a²

(d)

8a².

10.

The number of edges of a cube are

(a)

(b)

(c)

(d)

16.

11.

Identify the wrong statement of the following:

(a)

A square can be drawn on our notebook.

(b)

A circle can be drawn on the blackboard.

(c)

A rectangle can be drawn on a piece of paper.

(d)

A triangle cannot be drawn on a wall.

12.

Which of the following is a solid figure?

(a)

Circle

(b)

Cylinder

(c)

Square

(d)

Rectangle.

13.

Which of the following is a plane figure?

(a)

Cone

(b)

Square

(c)

Cylinder

(d)

Cube.

14.

There exists a pair of straight lines that are everywhere equidistant from one another' is a direct consequence of Euclid's

(a)

first postulate

(b)

second postulate

(c)

third postulate

(d)

fifth postulate

15.

John Playfair was a

(a)

french mathematician

(b)

Scottish mathematician

(c)

Indian mathematician

(d)

Egyptian mathematician

16.

Two interesting lines cannot be parallel to the same line, is started in the form of:

(a)

an axiom

(b)

a definition

(c)

a postulate

(d)

a proof

17.

If the point P lies in between M and N, and C is mid point of MP, then:

(a)

MC + PN + = MN

(b)

MP + CP = MN

(c)

MC + CN + MN

(d)

CP + CN = MN

18.

Given four points such that no three of them are collinear, then the number of lines that can be drawn through them is:

(a)

2 lines

(b)

4 lines

(c)

6 lines

(d)

8 lines

19.

Which one of the following statements is true?

(a)

Only one line can pass through a single point.

(b)

Three are an infinite number lines which pass through two distinct points.

(c)

two distinct lines cannot have more than one point in common.

(d)

If two circles are equal, then their radii are not equal.

20.

Select the wrong statement:

(a)

only one line can be pass through a single point.

(b)

Only one line can pass through two distinct points.

(c)

A terminated line can be produced indefinitely on both the sides.

(d)

if two circles are equal, then their radii are equal.

21.

Which of the following statement is incorrect?

(a)

A line segment has defined length

(b)

Three line are concurrent id and only if they have a common point

(c)

two lines drawn in a plane always intersected at a point

(d)

One and only one line can be drawn passing through a given point parallel to a given line

22.

The things which are double of same thing are:

(a)

equal

(b)

halves of same thing

(c)

unequal

(d)

double of the same thing

23.

The thing which coincide with one another are:

(a)

equal

(b)

unequal

(c)

half of some thinf

(d)

triple of one another

24.

Euclid stated that things which are equal to the same thing are equal to one another in the form of:

(a)

an axiom

(b)

a definition

(c)

a postulate

(d)

a proof

25.

The things which coincide with one another are:

(a)

equal to one another

(b)

un equal

(c)

double of same thing

(d)

triple of same thing

26.

Euclid stated that all right angles are equal to each other in the form of

(a)

an axiom

(b)

a definition

(c)

a postulate

(d)

a proof

27.

A proof is required for:

(a)

postulate

(b)

aximo

(c)

theorem

(d)

definition

28.

'Lines are parallel if they do not intersect' is stated in the form of:

(a)

an axiom

(b)

a definition

(c)

a postulate

(d)

a proof

29.

Two planes intersect each other to form a:

(a)

plane

(b)

Point

(c)

straight line

(d)

angle

30.

The number of line segments determined by three collinear points is:

(a)

two

(b)

Three

(c)

Only one

(d)

Four

31.

The number of lines that can pass through a given point is:

(a)

two

(b)

none

(c)

only one

(d)

infinite many

32.

How many numbers of lines do pass through two distinct points?

(a)

(b)

(c)

(d)

33.

Number of dimension(s) a surface:

(a)

(b)

(c)

(d)

34.

Pythagoras was a student of

(a)

Thales

(b)

Euclid

(c)

both (a) and (b)

(d)

Archimedes

35.

Euclid belonged to the country

(a)

Babylonia

(b)

Egypt

(c)

Greek

(d)

india

36.

In ancient India, alters with combination of shapes like rectangles, triangles and trapeziums were used for

(a)

public workship

(b)

household rituals

(c)

both (a) and (b)

(d)

none of the above

37.

In ancient India, the shapes of altars used for household rituals were

(a)

squares and circles

(b)

triangles and rectangles

(c)

trapeziums and phyramids

(d)

rectangles and squares

38.

In Indus Valley Civilisation (about 300 b.C), The brick used for construction work were having dimension in the ration

(a)

1 : 3 : 4

(b)

4 : 2 : 1

(c)

4 : 4 : 1

(d)

4 : 3 : 2

1 Marks

19 x 1 = 19

39.

The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4, then the ratio of their volumes will be _______________

40.

Two cylinders have bases of same size. The diameter of each is 7 cm. If one of the cylinder is 10 cm high and the other is 20 cm high, then the ratio of their volumes is _________________

41.

Find the volume of a right circular cone with radius 6 cm and height 7 cm.

42.

How many faces does a right circular cylinder have?

43.

The diameter of a football is five times the diameter of a criket ball. Ratio of surface areas of football and criket ball is _____________

44.

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

45.

If the number of square centimetres in the surface area of a shpere is equal to the number of cubic cm in its volume. find the diameter of the sphere?

46.

Compute the curved surface area of a hemishpere whose diameter is 14 cm.

47.

Calculate the volume of a cuboid whose dimensions are 3.6 cm, 8.2 am and 11 cm.

48.

Find the capacity of a tank of demensions 8 am \(\times\)6 cm \(\times\)2.5 cm.

49.

How can we identify parallel lines?

50.

Write the number of dimension(s) of a surface.

51.

What is a surface?

52.

Give any one example of a geometrical line from your surroundings.

53.

What is a straight line?

54.

How many lines can be passed through two distinct points?

55.

Explain when a system of axioms is called consistent.

56.

Express in variables the things which are double of the same thing.

57.

What does a theorem require?

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Answers Key:

Multiple Choice Question

38 x 1 = 38

Required number \(=\frac { 60\times 30\times 30 }{ 15\times 6\times 4 } =150\)

Number of cubes = \(\frac { { \left( 20 \right) }^{ 3 } }{ { \left( 5 \right) }^{ 3 } } =64\)

\(\frac { 2 }{ 3 } \times \left( 6\times 5\times 4 \right) 80{ m }^{ 3 }\)

v = 5 \(\times\) (6 \(\times\) 2 \(\times\) 1.5)

Volume = 15 \(\times\) 10 \(\times\) 8 = 1200 cm³

Length of the rod \(=\sqrt { { \left( 10 \right) }^{ 2 }+{ \left( 10 \right) }^{ 2 }+{ \left( 5 \right) }^{ 2 } } \)

(a)
4a²

(b)
6a²

10.

11.

(d)
A triangle cannot be drawn on a wall.

12.

(b)
Cylinder

13.

(b)
Square

14.

(d)
fifth postulate

15.

(b)
Scottish mathematician

16.

17.

18.

19.

20.

(a)
only one line can be pass through a single point.

21.

22.

(a)
equal

23.

(a)
equal

24.

(a)
an axiom

25.

(a)
equal to one another

26.

(a)
an axiom

27.

28.

(a)
an axiom

29.

30.

(b)
Three

31.

(d)
infinite many

32.

(a)
1

33.

34.

(a)
Thales

35.

36.

(a)
public workship

37.

(a)
squares and circles

38.

(b)
4 : 2 : 1

1 Marks

19 x 1 = 19

39.

()
Let radii of cylinders be 2x and 3x and heights be 5y and 3y respectively.
\(\therefore\) Ratio of volumes = \(\frac { \pi { (2x) }^{ 2 }\times 5y }{ \pi { (3x) }^{ 2 }\times 3y } \)
\(=\frac { { 4x }^{ 2 }\times 5 }{ { 9x }^{ 2 }\times 3 } \)
= 20:27.

40.

()
Let r denotes the radius of both cylinders and l and h be their heights respectively.
Ratio of their volumes = \(\frac { \pi { r }^{ 2 }h }{ \pi { r }^{ 2 }h' } =\frac { h }{ h' } =\frac { 10 }{ 20 } \)
= 1 : 2.

41.

()
Volume of right circular cone = \(\frac { 1 }{ 3 } \pi { r }^{ 2 }h\)
\(=\frac { 1 }{ 3 } \times \frac { 22 }{ 7 } \times { (6) }^{ 2 }\times 7=\frac { 1 }{ 3 } \times \frac { 22 }{ 7 } \times 36\times 7\)
= 264 cm³.

42.

()
3

43.

()
Given, diameter of football = 5 \(\times\) diameter of cricket ball
If r denotes radius of a football and r' that of a criket ball, then we have
2r = 5\(\times\)(2r')
\(\frac { 2r }{ 2r' } =5\)
or \(\frac { r }{ r' } =5\)
Now, ratio of surface areas\(=\frac { 4\pi { r }^{ 2 } }{ 4\pi { (r') }^{ 2 } } ={ \left( \frac { r }{ r' } \right) }^{ 2 }=\frac { 25 }{ 1 } \)
= 25 : 1

44.

()
Amount of water displaced = Volume of solid spherical ball
\(\therefore \ Volume\ of\ solid\ spherical\ ball=\frac { 4 }{ 3 } \pi { r }^{ 3 }\)
\(r=\frac { 4.2 }{ 2 } =2.1\) (given)
\(\therefore\) Volume of solid sperical ball=\(\frac { 4 }{ 3 } \pi ({ 2.1) }^{ 3 }\)
\(=\frac { 4 }{ 3 } \times \frac { 22 }{ 7 } \times { (2.1) }^{ 3 }\quad { cm }^{ 3 }\)
\(=\frac { 38808 }{ 1000 } litre\)
\(\therefore\) Amount of water displaced = 38808 litre (\(\because\)1 litre = 1000 cm³)

45.

()
Given, Area of Sphere=Volume of sphere
\(4\pi { r }^{ 2 }=\frac { 4 }{ 3 } \pi { r }^{ 3 }\)
where r is the radius of sphere
\(\Rightarrow\) r = 3 cm [on solving]
\(\therefore\) Diameter = 2r = 6 cm.

46.

()
Given diameter of hemisphere = 14 cm
\(\therefore\) radius = 7 cm
\(\therefore\) Curved surface area = 2\(\pi\)r²
\(=2\times \frac { 22 }{ 7 } \times 7\times 7\)
= 308 cm²

47.

()
Volume of cuboid = length\(\times\)breadth\(\times\)height
= 3.6\(\times\)8.2\(\times\)11
= 324.72 cm³.

48.

()
Capacity of the tank = 120 cm³
Capacity of the tank = length\(\times\)breadth\(\times\)height
= 8 cm\(\times\)6 cm\(\times\)2.5 cm
= 120 cm³

49.

()
Lines are parallel if they do not intersect on being extended.
For example:

Lines A and B are parallel lines.

50.

()
Dimension of surface= Length and Breadth (which is 2)

51.

()
A surface is that which has length and breadth.

52.

()
Meeting place of two walls.

53.

()
Two planes intersect each other to form a straight line.

54.

()
Only one line passes through two distinct points.

55.

()
A system of axioms is called consistent, when it is impossible to deduce from these axioms, a statement that contradicts any axiom or previously proved statement.

56.