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Construction of line segment and circle of given radius - class-VIII

Description: construction of line segment and circle of given radius
Number of Questions: 22
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Tags: basic geometrical concepts and shapes practical geometry line segment the circle lines, angles and shapes maths
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With the help of a normal ruler and a compass only, which of the following line segment is possible to construct?

  1. $2.1\ cm$

  2. $4.2\ cm$

  3. $5.43\ cm$

  4. $3.3\ cm$


Correct Option: A,B,D
Explanation:

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$.

So the lengths that can be measured are
$2.1\ \ cm,4.2\ \ cm$ and $3.3\ \ cm$
To measure $5.43$ we need a scale whose least count is $.001$

Which of the following line segments can be drawn with the help of a ruler and compass ?

  1. $1.234\ cm$

  2. $2.15\ cm$

  3. $2.5\ cm$

  4. $3.04\ cm$


Correct Option: C
Explanation:

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$

So only $2.5 \ \ cm$ can be measured using a ruler and compass.
Hence option $C$ is correct.

With the help of a normal ruler, which of the following line segment is possible to construct?

  1. $3.1\ cm$

  2. $4.234\ cm$

  3. $7.2\ cm$

  4. $1\ cm $


Correct Option: A,C,D
Explanation:

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$

So the lengths that can be measures are
$3.1\ \ cm$$,7.2\ \ cm$ and $1cm\ \ $
Options $A,C$ and $D$ are correct.

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes last?

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: A
Explanation:

For constructing a line segment of given length steps are following:

Step 1 : Draw a line(2).
Step 2 :Take a point $A$ anywhere on the line(4).
Step 3 : Extend the compass by keeping one end on the $0 \ \ cm$ mark and other at given length on ruler(3).
Step 4 :  Draw an arc on the line by keeping the pointed end of the compass on the point $A$ .Mark the arc point as $B.$(1)
So $1.$ is the last step.
Option $A$ is correct.


To construct a line segment of a given length, which of the following pairs of instruments are needed?

  1. Ruler and Protractor

  2. Ruler and Compass

  3. Compass and Divider

  4. Protractor and Divider


Correct Option: B
Explanation:

A line can be constructed using a Ruler and a Compass.

So option $B$ is correct.

Construct a line segment of length $8.4\ cm$. Divide this line into $3$ equal parts and find the length of each part.

  1. $2.4\ cm$

  2. $4.2\ cm$

  3. $1.8\ cm$

  4. $2.8\ cm$


Correct Option: D
Explanation:

Let length of each part $=x$

Lenght of three parts $=3x$
Given $3x=8.4$
$x=\dfrac{8.4}{3}=2.8$ cm

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes first?

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: B
Explanation:

Correct sequence is :

Step 1. Draw a line.
Step 2. Take a point $A$ anywhere on the line.
Step 3. Extend the compass by keeping one end on the $0 \ \ cm$ and other at the given length on the ruler.
Step 4. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc as point $B.$
So the first step is $2$
Option $B$ is correct.

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes second?

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: D
Explanation:

Correct sequence is :

Step 1. Draw a line.
Step 2. Take a point $A$ anywhere on the line.
Step 3. Extend the compass by keeping one end on the $0 \ \ cm$ and other at the given length on the ruler.
Step 4. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc as point $B.$
So the second step is $4$
Option $D$ is correct.

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes third?

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: C
Explanation:

Step 1 $:$ Draw a line .

Step 2 $:$ Take point $A$ anywhere on the line .
Step 3 $:$ Extend the compass by keeping one end on the $0\ \ cm$ mark at the given length of the rule.
Step 4 $:$ Draw an arc on the line by keeping the pointed end of the compass on the point $A$ .Mark the arc point as $B$
So $3$ is the third step .Option $C$ is correct.

State whether true/false
We can construct a copy of a line segment of length $2.345$ using scale/compass.

  1. True

  2. False


Correct Option: A
Explanation:

Yes, we can construct a copy of line segment of length $2.345$ using scale/compass. By using scale/compass we measure the length and by stretching the compass & cut the same length of line.

Steps of constructing a line segment equal to the length of given segment is written in jumbled form below:
1. Draw a line $l$. Mark a point $A$ on line $l$. Without changing compass's setting, place the compass at $A$.
2. Make an arc on the line $l$ which cuts $l$ at $B$. Now, $AB$ is a copy of $CD$.
3. Draw a line segment $CD$ of any length.
4. Fix the compass's end on $C$ and pencil on $D$. This gives the length of $CD$.

Which of the above comes last.

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: B
Explanation:

Correct sequence is :

Step 1. Draw a line segment $CD$ of any length.
Step 2 .Fix the compass's end on $C$ and a pencil on $D$. This gives length $CD.$
Step 3. Draw a line $l$. Mark a point $A$ on line $l$.Without changing compass's setting place the compass at $A$
Step 4. Make an arc on the line $l$ whcih cuts $l$ at $B$  Now $AB$ is a copy of $CD$
So the last step is $2$
Option $B$ is correct.

Which of the following line segments cannot be drawn with the help of a ruler and compass ?

  1. $3.153\ cm$

  2. $4.3\ cm$

  3. $5.2\ cm$

  4. $6.1\ cm$


Correct Option: A
Explanation:

Line segment of length $3.153\ \ cm$ can not be drawn using a compass as the least count of the compass is $1\ \ mm$ or $.1\ \ cm$

So option $A$ is corrrect.

Construct a line segment of length $12.4\ cm$. Divide this line into $4$ equal parts and find the length of each part.

  1. $3.1\ cm$

  2. $4.1\ cm$

  3. $3.0\ cm$

  4. $4.0\ cm$


Correct Option: A
Explanation:

$1.$ Draw a line segment of length $12.4\ \ cm$ using a ruler.

Now we have to divide the length into four parts . So we have to divide the length by $4$
Lenght of each part $\dfrac{12.4}{4}=3.1\ \ cm$
$2.$ Now open the compass to $3.1\ \ cm$ and cut an arc on the line by placing the needle on one end on the line and mark the point as $B$.
$3.$ Repeat the step $2.$ by placing the compass on point $B$
Length of each part $=3.1\ \ cm$
So option $C$ is correct.

Steps of constructing a line segment equal to the length of given segment is written in jumbled form below:
1. Draw a line $l$. Mark a point $A$ on line $l$. Without changing compass's setting, place the compass at $A$.
2. Make an arc on the line $l$ which cuts $l$ at $B$. Now, $AB$ is a copy of $CD$.
3. Draw a line segment $CD$ of any length.
4. Fix the compass's end on $C$ and pencil on $D$. This gives the length of $CD$.
Arrange them in correct order.

  1. $3,4,1,2$

  2. $1,2,3,4$

  3. $4,3,2,1$

  4. $3,1,2,4$


Correct Option: A
Explanation:

Correct sequence is :

Step 1. Draw a line segment $CD$ of any length.
Step 2 .Fix the compass's end on $C$ and a pencil on $D$. This gives length $CD.$
Step 3. Draw a line $l$. Mark a point $A$ on line $l$.Without changing compass's setting place the compass at $A$
Step 4. Make an arc on the line $l$ whcih cuts $l$ at $B$  Now $AB$ is a copy of $CD$
So the sequence is $3,4,1,2$

Construct a line segment of length $4.6\ cm$. Divide this line into $2$ equal parts and find the length of each part.

  1. $2.0\ cm$

  2. $2.1\ cm$

  3. $2.2\ cm$

  4. $2.3\ cm$


Correct Option: D
Explanation:
steps of construction :
1 . draw a line of length 4.6 cm using ruler .
2. Place the compass at one end of line segment.
3 . Adjust the compass to slightly longer than half the line segment length.
4. Draw arcs above and below the line.
 5 .Keeping the same compass width, draw arcs from other end of line.
6 . Place ruler where the arcs cross, and draw the line segment.
7. drawn line segment cuts the initial line segment  into two equal parts .
8. measure the bisected length using ruler thats comes out be $= \dfrac{1}{2} \times 4.6 = 2.3 cm$

Draw a line $AB=7.8\ cm$, what will be the $\dfrac{2}{3}$rd of $AB$.

  1. $11.7\ cm$

  2. $5.2\ cm$

  3. $3.9\ cm$

  4. $2.6\ cm$


Correct Option: B
Explanation:

Draw a line segment $AB$ of $7.8\ \ cm$ using ruler 

.$\dfrac{2}{3}AB=$ $=\dfrac { 2 }{ 3 } \times 7.8=5.2 \ cm$
Option $B$ is correct.

Construct a line $AB=6.5\ cm$. What will be the $\dfrac{1}{5}$th of $AB$ ?

  1. $4.2\ cm$

  2. $3.5\ cm$

  3. $2.4\ cm$

  4. $1.3\ cm$


Correct Option: D
Explanation:

Draw a line segment $AB$ of length $6.5\ \ cm$

$\dfrac { 1 }{ 5 } AB=\dfrac { 1 }{ 5 } \times 6.5=1.3\ \ cm$
So option $D$ is correct.

Draw a line $XY=13.6\ cm$. what will be the $\dfrac{1}{4}$th of $XY$ ?

  1. $6.8\ cm$

  2. $5.2\ cm$

  3. $3.4\ cm$

  4. $2.2\ cm$


Correct Option: C
Explanation:

Draw a line segment $XY$ of length $13.6\ \ cm$

$\dfrac { 1 }{ 4 } XY=\dfrac { 1 }{ 4 } \times 13.6=3.4\ \ cm$
Option $C$ is correct.

Draw a line $PQ=9.6\ cm$. What will be the $\dfrac{1}{3}$rd of $PQ$ ?

  1. $3.2\ cm$

  2. $4.6\ cm$

  3. $2.4\ cm$

  4. $2.5\ cm$


Correct Option: A
Explanation:

Draw a line segment $PQ$ is length $9.6\ \ cm$ using a ruler.

$\dfrac { 1 }{ 3 } PQ=\dfrac { 1 }{ 3 } \times 9.6=3.2\ \ cm$
So option $A$ is correct.

Use your compasses to draw a circle of radius as specified below. What is the diameter of each of these circles.

  1. $5\ cm$

  2. $4\ cm$

  3. $12\ cm$

  4. $7\ cm$


Correct Option: A

Steps of constructing a line segment equal to the length of given segment is written in jumbled form below:
1. Draw a line $l$. Mark a point $A$ on line $l$. Without changing compass's setting, place the compass at $A$.
2. Make an arc on the line $l$ which cuts $l$ at $B$. Now, $AB$ is a copy of $CD$.
3. Draw a line segment $CD$ of any length.
4. Fix the compass's end on $C$ and pencil on $D$. This gives the length of $CD$.

Which of the above comes first.

  1. $1$

  2. $2$

  3. $3$

  4. $4$


Correct Option: C
Explanation:

Correct sequence is :

Step 1. Draw a line segment $CD$ of any length.
Step 2 .Fix the compass's end on $C$ and a pencil on $D$. This gives length $CD.$
Step 3. Draw a line $l$. Mark a point $A$ on line $l$.Without changing compass's setting place the compass at $A$
Step 4. Make an arc on the line $l$ whcih cuts $l$ at $B$  Now $AB$ is a copy of $CD$
So the first step is $3$
Option $C$ is correct.

Choose the correct answer from the alternatives given.
Water is flowing at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank which is $50$ m long, $44$ m wide. The time taken (in hours) for the rise in the level of water in the tank to be $7$ cm is

  1. $2$

  2. $1\dfrac{1}{2}$

  3. $3$

  4. $2\dfrac{1}{2}$


Correct Option: A
Explanation:

Water
flowed by the pipe in lh = $\pi r^2h$
= $\dfrac{22}{7} \times$ $\dfrac{7\times 7}{100\times100}$ $\times 5000 m^3 =77m^3$
Volume
of expected water in the tank = $\frac{50 \times 44 \times 7}{100} = 154
m^3$ 
Required
time= $154/77 = 2 hrs$.

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