### Chapter - 5 Understanding Elementary Shapes

Q
##### Understanding Elementary Shapes

Question:

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: (a) When the hour hand of a clock goes from 3 to 9, it will make a straight angle of 1800.

We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, Fraction = $\frac{180^{\circ}}{360^{\circ}} = \frac{1}{2}$

(b) When the hour hand of a clock goes from 4 to 7, it will make a right angle of 900.

We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, Fraction = $\frac{90^{\circ}}{360^{\circ}} = \frac{1}{4}$

(c) When the hour hand of a clock goes from 7 to 10, it will make a right angle of 900.

We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, Fraction = $\frac{90^{\circ}}{360^{\circ}} = \frac{1}{4}$

(d) When the hour hand of a clock goes from 12 to 9, it will make 3 right angle which equal to 2700.

We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, Fraction = $\frac{270^{\circ}}{360^{\circ}} = \frac{3}{4}$

(e) When the hour hand of a clock goes from 1 to 10, it will make 3 right angle which equal to 2700.

We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, Fraction = $\frac{270^{\circ}}{360^{\circ}} = \frac{3}{4}$

(f) When the hour hand of a clock goes from 6 to 3, it will make 3 right angle which equal to 2700.

We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, Fraction = $\frac{270^{\circ}}{360^{\circ}} = \frac{3}{4}$

2. Where will the hand of a clock stop if it

(a) starts at 12 and makes $\frac{1}{2}$ of a revolution, clockwise?

(b) starts at 2 and makes $\frac{1}{2}$ of a revolution, clockwise?

(c) starts at 5 and makes $\frac{1}{4}$ of a revolution, clockwise?

(d) starts at 5 and makes $\frac{3}{4}$ of a revolution, clockwise?

Solution: (a) We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, $\frac{1}{2}\ revolution = \frac{360^{\circ}}{2} = 180^{\circ}$

When hour hand starts at 12 after 1/2 revolution it rotates 1800.

Hence, hour hand will reach at 6 after 1/2 revolution.

(b) We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, $\frac{1}{2}\ revolution = \frac{360^{\circ}}{2} = 180^{\circ}$

When hour hand starts at 2 after 1/2 revolution it rotates 1800.

Hence, hour hand will reach at 8 after 1/2 revolution.

(c) We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, $\frac{1}{4}\ revolution = \frac{360^{\circ}}{4} = 90^{\circ}$

When hour hand starts at 5 after 1/4 revolution it rotates 900.

Hence, hour hand will reach at 8 after 1/4 revolution.

(d) We know that in one complete clockwise revolution, hour hand will rotate 3600.

So, $\frac{3}{4}\ revolution = \frac{3}{4} \times 360^{\circ} = 270^{\circ}$

When hour hand starts at 5 after 3/4 revolution it rotates 1800.

Hence, hour hand will reach at 2 after 3/4 revolution.

3. Which direction will you face if you start facing

(a) east and make $\frac{1}{2}$ of a revolution clockwise?

(b) east and make $1\frac{1}{2}$ of a revolution clockwise?

(c) west and make $\frac{3}{4}$ 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: Revolving one complete circle will makes 360and the angle between two adjacent sides is 900 which is in fraction is $\frac{1}{4}$ as shown in the diagram below.

(a) If we start facing towards east and make $\frac{1}{2}$ of a revolution clockwise, then we will face towards west direction.

(b)  If we start facing towards east and make $1\frac{1}{2}$ of a revolution clockwise, then we will face towards west direction.

(c)  If we start facing towards west and make $\frac{3}{4}$ of a revolution anti-clockwise, then we will face towards north direction.

(d)  If we start facing towards south and make one full revolution, then we will face towards south direction again.

There is no need to specify clockwise or anti-clockwise as in both cases after one revolution we will face in the same direction that is south.

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: Revolving one complete circle will makes 360and the angle between two adjacent sides is 900 which is in fraction is $\frac{1}{4}$ as shown in the diagram below.

(a) If we start facing towards east and turn clockwise to face north, we have to make $\frac{3}{4}$ of a revolution.

(b) If we start facing towards south and turn clockwise to face east, we have to make $\frac{3}{4}$ of a revolution.

(c) If we start facing towards west and turn clockwise to face east, we have to make $\frac{1}{2}$ 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: We know that in one complete clockwise revolution, hour hand will rotate 3600.

(a) When the hour hand of a clock goes from 3 to 6, it will revolve by 900 which is equal to 1 right angle.

(b) When the hour hand of a clock goes from 2 to 8, it will revolve by 1800 which is equal to 2 right angle.

(c) When the hour hand of a clock goes from 5 to 11, it will revolve by 1800 which is equal to 2 right angle.

(d) When the hour hand of a clock goes from 10 to 1, it will revolve by 900 which is equal to 1 right angle.

(e) When the hour hand of a clock goes from 12 to 9, it will revolve by 2700 which is equal to 3 right angle.

(f) When the hour hand of a clock goes from 12 to 6, it will revolve by 1800 which is equal to 2 right angle.

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: Revolving one complete circle will makes 360and the angle between two adjacent sides is 900 which is in fraction is $\frac{1}{4}$ as shown in the diagram below.

(a) If we start facing towards south and turn clockwise to face west, we have to make 1 right angle.

(b) If we start facing towards north and turn anti-clockwise to face east, we have to make 3 right angle.

(c) If we start facing towards west and turn to west, we have to make one complete revolution 3600 which is equal to 4 right angle.

(d) If we start facing towards south and turn to face north either clockwise or anti-clockwise, we have to make 2 right angle.

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: We know that in one complete clockwise revolution, hour hand will rotate 3600.

(a) When hour hand starts from 6 after 1 right angle revolution it rotates 900.

Hence, hour hand will stop at 9.

(b) When hour hand starts from 8 after 2 right angle revolution it rotates 1800.

Hence, hour hand will stop at 2.

(c) When hour hand starts from 10 after 3 right angle revolution it rotates 2700.

Hence, hour hand will stop at 7.

(d) When hour hand starts from 7 after 2 straight angle revolution it rotates 3600.

Hence, hour hand will stop at 7 again.