**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)** of a revolution**(b)** of a revolution**(c)** of a revolution**(d)** of a revolution**(e)** of a revolution**(f)** of a revolution

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

**(a)**starts at 12 and makes of a revolution, clockwise?

**(b)**starts at 2 and makes of a revolution clockwise?

**(c)**starts at 5 and makes of a revolution, clockwise?

**(d)**starts at 5 and makes of a revolution, clockwise?

**Solution:****(a)** If the hand of clock starts at 12 and makes of a revolution clockwise it reaches at 6.**(b)** If the hand of clock starts at 2 and makes of a revolution clockwise it reaches at 8.**(c)** If the hand of clock starts at 5 and makes of a revolution clockwise it reaches at 8.**(d)** If the hand of clock starts at 5 and makes of a revolution clockwise it reaches at 2.

**Question 3.Which direction will you face if you start facing**

**(a)**east and make of a revolution clockwise?

**(b)**east and make 1 of a revolution clockwise?

**(c)**west and make of a revolution anti-clockwise?

**(d)**south and make one full revolution?

(Should we specify clockwise or anit-clockwise for this last question? Why nor?)

**Solution:****(a)** Facing east and on making of a revolution clockwise, we will face west.

**(b)** Facing east and on making 1 of a revolution clockwise, we will face west.**(c)** Facing west and on making of a revolution anti-clockwise, we will face north.

**Facing south and on making 1 full revolution we will face south again.**

(d)

(d)

There is no need to specify clockwise or anti-clockwise in the last question as turning by one full revolution (i.e., two straight angles) make us to reach the original position.

**Question 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:**

Figures drawn will dearly show the amount of revolution:**(a)** of a revolution**(b)** of a revolution

**(c)** of a revolution

**Question 5.Find the number of right angles turned through by the hour hand of 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:**

Since turning by two straight angles (or four right angles) in the same direction makes a full turn. Thus for the movement of clock hand from 12 – 1,1 – 2, 2 – 3, … 11 – 12 i.e., 12 in number gives 4 right angles turn. Therefore,**(a)** From 3 to 6 : 3 – 4, 4 – 5 and 5 – 6 i.e., 3 in number.

∴ Number of right angles turned through by the hour hand of a clock when it goes from 3 to 6

= right angles = 1 right angles

**(b)** From 2 to 8 :2 – 3,3 – 4, 4 – 5, 5 – 6,6 – 7 and 7 – 8 i.e., 6 in number.

∴ Number of right angles turned through by the hour hand of a clock

when it goes from 2 to 8

= right angles = 2 right angles

**(c)** From 5 to II : 5 – 6, 6 – 7, 7 – 8, 8 – 9, 9 – 10 and 10 – 11 i.e., 6 in number.

∴ Number of right angles turned through by the hour hand of a clock when it goes from 5 to 11

= right angles = 2 right angles

**(d)** From 10 to 1 :10 – 11,11 -12 and 12 – 1 i.e., 3 in number.

∴ Number of right angles turned through by the hour hand of a clock when it goes from 10 to 1

= right angles = 1 right angles

**(e)** From 12 to 9 : 12 – 1, 1 – 2, 2 – 3, 3 – 4, 4 – 5, 5 – 6, 6 – 7, 7 – 8 and 8 – 9 i.e., 9 in number

∴ Number of right angles turned through by the hour hand of a clock when it goes from 12 to 9

= right angles = 1 right angles

**(f)** From 12 to- 6 : 12 – 1, 1 – 2, 2 – 3, 3 – 4, 4 – 5 and 5 – 6 i.e., 6 in number.

∴ Number of right angles turned through by the hour hand of a clock when it goes from 12 to 6

= right angles = 2 right angles

**Question 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:**

Figures drawn will clearly indicate the number of right angles we make if we start facing:**(a)** south and turn clockwise to west is 1 right angle.**(b)** north and turn anti-clockwise to east are 3 right angles.

**(c)** west and turn to west are 4 right angles.**(d)** south and turn to north are 2 right angles.

**Question 7.Where will the hour hand qfa 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 12 hours hour hand turns through 4 right angles i.e., in a turn of 1 right angle, the hour hand moves 3 hours.**(a)** If the hour hand of a clock starts from 6 and turns through 1 right angle then its hour hand stops at (6 +3) i.e., 9.**(b)** If the hour hand of a clock starts from 8 and turns through 2 right

angles then its hour hand stops at (8 + 2 x 3) = 14 i.e., 2. .**(c)** If the hour hand of a clock starts from 10 and turns through 3 right angles then its hour hand stops at (10+3×3) = 19 i.e., 7.**(d)** If the hour hand of a clock starts from 7 and turns through 2 straight angles i.e., 4 right angles then its hour hand stops at (7 + 4 x 3) = 19 i.e., 7.