GSEB Class 6 Maths Solutions Chapter 5 Understanding Elementary Shapes Exercise 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
Answer:
(a) From 3 to 9: The hour hand turning from 3 to 9 makes \( \frac {1}{2} \) of a revolution.

Exam Tip: One full revolution of an hour hand is 12 hours. So, each hour covers \( \frac{1}{12} \) of a revolution.

(b) From 4 to 7: The hour hand turning from 4 to 7 makes \( \frac{1}{4} \) of a revolution.

Exam Tip: To find the fraction of a revolution, divide the number of hours moved by 12 (total hours in a full clock face).

(c) From 7 to 10: The hour hand turning from 7 to 10 makes \( \frac{1}{4} \) of a revolution.

Exam Tip: Remember that 3 hours of movement for an hour hand equals a quarter of a revolution, or one right angle.

(d) From 12 to 9: The hour hand turning from 12 to 9 makes \( \frac{3}{4} \) of a revolution.

Exam Tip: For turns larger than a half-revolution, it's often simpler to calculate the remaining portion to complete a full circle.

(e) From 1 to 10: The hour hand turning from 1 to 10 makes \( \frac{3}{4} \) of a revolution.

Exam Tip: Visualizing the clock face helps greatly; mentally move the hand and count the hours.

(f) From 6 to 3: The hour hand moving from 6 to 3 turns through \( \frac{3}{4} \) of a revolution.

Exam Tip: Converting the number of hours into a fraction of 12 hours gives the revolution fraction.

Question 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?
Answer:
The clock hand starting:
(a) from 12 and making \( \frac { 1 }{ 2 } \) of a revolution reaches at 6.

Exam Tip: A half revolution means moving 6 hours forward. Count 6 hours clockwise from the starting point.

(b) from 2 and making \( \frac {1}{ 2 } \) of a revolution reaches at 8.

Exam Tip: Understand that \( \frac{1}{2} \) of a revolution is equivalent to 6 hours on a clock face.

(c) from 5 and making \( \frac {1}{ 4 } \) of a revolution reaches at 8.

Exam Tip: A quarter revolution means moving 3 hours forward. From 5, 3 hours clockwise takes you to 8.

(d) from 5 and making \( \frac {3}{ 4 } \) of a revolution reaches at 2.

Exam Tip: Three-quarters of a revolution means moving 9 hours forward. From 5, 9 hours clockwise takes you to 2.

Question 3. What direction will you face if you start facing
(i) (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?
(ii) Should we specify clockwise or anti-clockwise
Answer:
(i) From the figure, we can say that the facing will be towards:
(a) West

Exam Tip: A half revolution from East, clockwise, brings you to West.

(b) West

Exam Tip: A full revolution brings you back to the start. \( 1\frac{1}{2} \) revolution means one full turn plus a half turn. Starting East, a full turn ends East, then half a turn ends West.

(c) North

Exam Tip: Anti-clockwise turns go opposite to clock movement. Three-quarters of a revolution is three right angles.

(d) South

Exam Tip: One full revolution always brings you back to your starting point, regardless of the direction of turn.

(ii) Yes, it is important to state if the turn is clockwise or anti-clockwise when talking about a revolution. This is because the way you turn changes your final spot. Without knowing the direction, the end location of the turn cannot be figured out correctly, because spinning one way gives a different outcome than spinning the same amount the other way.
In simple words: Yes, always say if you're turning clockwise or anti-clockwise. The direction changes where you end up, so you need to know it to find the correct final position.

Exam Tip: Always clearly specify the direction of rotation (clockwise or anti-clockwise) when describing turns to avoid confusion.

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?
Answer:
(a) Starting from east and reaching at north (turning clockwise). \( \frac { 3 }{ 4 } \) of a revolution is required.

Exam Tip: Moving from East clockwise to North covers three right angles, which is \( \frac{3}{4} \) of a full revolution.

(b) Starting from south and turning clockwise up to east, \( \frac { 3 }{ 4 } \) of a revolution is required.

Exam Tip: Visualize the direction of turns on a compass to easily determine the fraction of a revolution.

(c) Starting from west and turning clockwise up to east \( \frac { 1 }{ 2 } \) of a revolution is required.

Exam Tip: Facing West and turning clockwise to face East is a direct reversal, which means half a revolution.

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
Answer:
(a) From 3 to 6: The hour hand turning from 3 to 6 turns through 1 right angle.

Exam Tip: Moving 3 hours on a clock face always corresponds to turning through one right angle (90 degrees).

(b) From 2 to 8: The hour hand turning from 2 to 8 turns through 2 right angles.

Exam Tip: Two right angles means half a revolution, or 6 hours of movement.

(c) From 5 to 11: The hour hand turning from 5 to 11 turns through 2 right angles.

Exam Tip: Recognize that 6 hours of movement equals 180 degrees, which is two right angles.

(d) From 10 to 1: The hour hand turning from 10 to 1 turns through 1 right angle.

Exam Tip: A movement of 3 hours on a clock face, whether from 10 to 1 or any other 3-hour span, represents one right angle.

(e) From 12 to 9: The hour hand turning from 12 to 9 turns through 3 right angles.

Exam Tip: Three right angles represent \( \frac{3}{4} \) of a full circle, or 9 hours of movement on a clock.

(f) From 12 to 6: The hour hand turning from 12 to 6 turns through 2 right angles.

Exam Tip: A turn from 12 to 6, clockwise, is exactly half a circle, which equals two 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?
Answer:
(a) From the figure, we observe that turning clockwise from south to west, we make 1 right angle.

Exam Tip: Each quarter turn on a compass (e.g., South to West clockwise) is one right angle.

(b) From the figure, we find that turning anti-clockwise from north to east, we make 3 right angles.

Exam Tip: Anti-clockwise from North to East means passing West and South first, covering three right angles.

(c) From the figure, we find that turning [clockwise or anti-clockwise] from west to west, we make 4 right angles.

Exam Tip: A full circle (returning to the same direction) always accounts for four right angles.

(d) From the figure, we find that turning [clockwise or anti-clockwise] from south to north, we make 2 right angles.

Exam Tip: Turning from South to North is a half-turn (straight angle), which means two right angles.

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?
Answer:
(a) Starting from 6 and turning through 1 right angle, the hour hand will reach at 9.

Exam Tip: One right angle on a clock means moving 3 hours forward. From 6, moving 3 hours clockwise brings you to 9.

(b) Starting from 8 and turning through 2 right angles, the hour hand will reach at 2.

Exam Tip: Two right angles means moving 6 hours forward (half a circle). From 8, 6 hours clockwise takes you to 2.

(c) Starting from 10 and turning through 3 right angles, the hour hand will reach at 7.

Exam Tip: Three right angles means moving 9 hours forward. From 10, 9 hours clockwise takes you to 7.

(d) Starting from 7 and turning through 2 straight angles, the hour hand will reach at 7. Note: 2 straight angles = 4 right angles

Exam Tip: Two straight angles (or 4 right angles) means a full revolution, bringing the hand back to its starting position.