## Understanding Elementary Shapes

## Exercise – 5.2

**Ex 5.2 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) 3 to 9

9 – 3 = 6 ÷ 12 = of a revolution

(b) 4 to 7

7 – 4 = 3 ÷ 12 = of a revolution

(c) 7 to 10

10 – 7 = 3 ÷ 12 = of a revolution

(d) 12 to 9= 0 to 9

9 – 0 = 9 ÷ 12 = of a revolution

(e) 1 to 10

10 – 1 = 9 ÷ 12 = of a revolution

(f) 6 to 3 = 6 to 12 and then 12 to 3

6 to 12 = 12 – 6 = 6 and 12 to 3 = 0 to 3 = 3 – 0 = 3

6 + 3 = 9 ÷ 12 = of a revolution

**Ex 5.2 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) Starting from 12 and making of a revolution, then the clock hand stops at 6.

(b) Starting from 2 and making of a revolution, then the clock hand stops at 8.

(c) Starting from 5 and making of a revolution, then the clock hand stops at 8.

(d) Starting from 5 and making of a revolution, then the clock hand stops at 2.

**Ex 5.2 Question 3.**

**Which direction will you face if you start facing**

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

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

**(c) west and make of a revolution anticlockwise?**

**(d) south and make one full revolution? (Should we specify clockwise or anticlockwise for this last question? Why not?)**

**Solution:**

Taking one full revolution we will reach back to the original (starting) position. Therefore, it makes no difference whether we turn clockwise or anticlockwise.

**Ex 5.2 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:**

(a) If we start from east and reach north (turning clockwise) of a revolution is required.

(b) If we start from south turning clockwise to face east, of a revolution, is required.

(c) If we start from west turning clockwise to face east, of a revolution is required.

**Ex 5.2 Question 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:**

(a) 3 to 6

Starting from 3 to 6, the hour hand turns through 90^{0 }or 1 right angle.

(b) 2 to 8

Starting from 2 to 8, the hour hand turns through 180^{0} or 2 right angles.

(c) 5 to 11

Starting from 5 to 11, the hour hand turns through 180^{0} or 2 right angles.

(d) 10 to 1

Starting from 10 to 1, the hour hand turns through 90^{0} or 1 right angle.

(e) 12 to 9

Starting from 12 to 9, the hour hand turns through 270^{0} or 3 right angles.

(f) 12 to 6

Starting from 12 to 6, the hour hand turns through 180^{0} or 2 right angles.

**Ex 5.2 Question 6.**

**How many right angles do you make if you start facing**

**(a) south and turn clockwise to west?**

**(b) north and turn anticlockwise to east?**

**(c) west and turn to west?**

**(d) south and turn to north?**

**Solution:**

**Ex 5.2 Question 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:**

(a) Starting from 6 and turning through 90^{0} or 1 right angle, the hour hand stops at 9.

(b) Starting from 8 and turning through 180^{0} or 2 right angles, the hour hand stops at 2.

(c) Starting from 10 and turning through 270^{0} or 3 right angles, the hour hand stops at 7.

(d) Starting from 7 and turning through 180^{0} or 2 right angles, the hour hand stops at 7.