Chapter - 5- EXERCISE 5.2 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

1. What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
                  (a) 3 to 9                                (b) 4 to 7                     (c) 7 to 10                                                                (d) 12 to 9                              (e) 1 to 10                   (f) 6 to 3

Solution/Explanation:

a)Fraction=18003600=12${\displaystyle \frac{{180}^0}{{360}^0}=\frac{1}{2}}$
b)Fraction=9003600=14${\displaystyle \frac{{90}^0}{{360}^0}=\frac{1}{4}}$
c)Fraction=9003600=14${\displaystyle \frac{{90}^0}{{360}^0}=\frac{1}{4}}$
d)Fraction=27003600=34${\displaystyle \frac{{270}^0}{{360}^0}=\frac{3}{4}}$
e)Fraction=27003600=34${\displaystyle \frac{{270}^0}{{360}^0}=\frac{3}{4}}$
f)Fraction=27003600=34${\displaystyle \frac{{270}^0}{{360}^0}=\frac{3}{4}}$.

2. Where will the hand of a clock stop if it 
(a) starts at 12 and makes 1/2 of a revolution, clockwise? 

(b) starts at 2 and makes 1/2 of a revolution, clockwise?

 (c) starts at 5 and makes 1/4 of a revolution, clockwise?

 (d) starts at 5 and makes 3/4 of a revolution, clockwise?

Solution/Explanation:

In 1 complete clockwise revolution, the hand of a clock will rotate by 3600

(a) If the hand of a clock starts at 12 and makes 1/2 of a revolution clockwise, then it will

rotate by 180 degree and hence, it will stop at 6.

 (b) If the hand of a clock starts at 2 and makes 1/2 of a revolution clockwise, then it will

rotate by 180 degree and hence, it will stop at 8.

(c) If the hand of a clock starts at 5 and makes 1/4 of a revolution clockwise, then it will

rotate by 90 degree and hence, it will stop at 8.

(d) If the hand of a clock starts at 5 and makes 3/4 of a revolution clockwise, then it will

rotate by 270 degree and hence, it will stop at 2.

3. Which direction will you face if you start facing 

(a) east and make 1/2 of a revolution clockwise?

(b) east and make  of a revolution clockwise?

(c) west and make 3/4 of a revolution anti-clockwise?

(d) south and make one full revolution?

(Should we specify clockwise or anti-clockwise for this last question? Why not?)

Solution/Explanation:

a)      When you start facing east and make ½ of a revolution, you revolve by 180°. Hence, you would be facing west.

b)      When you start facing east and make 1 revolution clockwise, you face east again. Then you make another ½ of a revolution, that is, 180°. Hence, you would be facing west.

c)      When you start facing west and make ¾ of a revolution anti-clockwise, you revolve by 270°. This is by 180° and then by 90°. When you revolve by 180° anti-clockwise you face east and then you revolve by 90° anti-clockwise, you face north.

d)     When you start facing south and make a full revolution, that is 360°, you will again face the south. The direction, whether clockwise or anticlockwise, does not matter in this case because a full revolution will bring back to the initial position.

4. What part of a revolution have you turned through if you stand facing 

(a) east and turn clockwise to face north? 

(b) south and turn clockwise to face east? 

(c) west and turn clockwise to face east?

Solution/Explanation:

If we revolve one complete round in either clockwise or anti-clockwise direction, then we will

revolve by 360 degree and the two adjacent directions will be at 90 degree or 1/4 of a

complete revolution away from each other.

(a) If we start facing East and turn clockwise to face North, then we have to make 3/4 of a revolution.

(b) If we start facing West and turn clockwise to face East, then we have to make 1/2 of a revolution.

5. Find the number of right angles turned through by the hour hand of a clock when it goes from 

(a) 3 to 6                  (b) 2 to 8             (c) 5 to 11             (d) 10 to 1 (e) 12 to 9                (f) 12 to 6

Solution/Explanation:

a)6-3=3 hours,means 14⋅3600=900${\displaystyle \frac{1}{4}\cdot {360}^0={90}^0}$
one right angled triangle
b)8-2=6 hours,means 12⋅3600=18000${\displaystyle \frac{1}{2}\cdot {360}^0={1800}^0}$
two right angled triangle

c)11-5=3 hours,means 12⋅3600=1800${\displaystyle \frac{1}{2}\cdot {360}^0={180}^0}$

two right angled triangle
d)13-10=3 hours,means 14⋅3600=900${\displaystyle \frac{1}{4}\cdot {360}^0={90}^0}$
one right angled triangle
e)9-0=9 hours,means 34⋅3600=2700${\displaystyle \frac{3}{4}\cdot {360}^0={270}^0}$
three right angled triangle
f)12-6=6 hours,means 12⋅3600=1800${\displaystyle \frac{1}{2}\cdot {360}^0={180}^0}$
two right angled triangle

6. How many right angles do you make if you start facing (a) south and turn clockwise to west? (b) north and turn anti-clockwise to east? (c) west and turn to west? (d) south and turn to north?

Solution/Explanation:

If we revolve one complete round in either clockwise or anti clockwise direction, then we will

revolve by 360 degree or 4 right angles and the two adjacent directions will be at 90 degree or

1 right angle away from each other.

(a) If we start facing South and turn clockwise to West, then we make 1 right angle.

(b) If we start facing North and turn anti clockwise to East, then we make 2 right angles.

(c) If we start facing West and turn to West, then we make 1 complete round or 4 right angles.

(d) If we start facing South and turn to West, then we make 2 right angles.

7. Where will the hour hand of a clock stop if it starts 
  (a) from 6 and turns through 1 right angle?
  (b) from 8 and turns through 2 right angles? 
  (c) from 10 and turns through 3 right angles?
  (d) from 7 and turns through 2 straight angles?

Solution/Explanation:

In 1 complete revolution (clockwise or anti clockwise), the hour hand of a clock will rotate by

360 degree or 4 right angles.

(a) If the hour hand of a clock starts from 6 and turns through 1 right angle, then it will stop at 9.

(b) If the hour hand of a clock starts from 8 and turns through 3 right angles, then it will stop at 2.

(c) If the hour hand of a clock starts from 10 and turns through 3 right angles, then it will stop at 7.

(d) If the hour hand of a clock starts from 7 and turns through 2 straight angles, then it will stop at 7