Class 6 Maths NCERT Solutions for Chapter 5 Understanding Elementary Shapes Ex – 5.2

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) \frac { 1 }{ 2 }  of a revolution
(b) \frac { 1 }{ 4 }  of a revolution
(c) \frac { 1 }{ 4 }  of a revolution
(d) \frac { 3 }{ 4 }  of a revolution
(e) \frac { 3 }{ 4 }  of a revolution
(f) \frac { 3 }{ 4 }  of a revolution

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?

Solution:
(a) If the hand of clock starts at 12 and makes \frac { 1 }{ 2 }  of a revolution clockwise it reaches at 6.
(b) If the hand of clock starts at 2 and makes \frac { 1 }{ 2 }  of a revolution clockwise it reaches at 8.
(c) If the hand of clock starts at 5 and makes \frac { 1 }{ 4 }  of a revolution clockwise it reaches at 8.
(d) If the hand of clock starts at 5 and makes \frac { 3 }{ 4 }  of a revolution clockwise it reaches at 2.

Question 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 anit-clockwise for this last question? Why nor?)

Solution:
(a) Facing east and on making \frac { 1 }{ 2 }  of a revolution clockwise, we will face west.

(b) Facing east and on making 1\frac { 1 }{ 2 }  of a revolution clockwise, we will face west.

(c)
 Facing west and on making \frac { 3 }{ 4 }  of a revolution anti-clockwise, we will face north.

(d)
 Facing south and on making 1 full revolution we will face south again.
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.
tiwari academy class 6 maths Chapter 5 Understanding Elementary Shapes 8

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) \frac { 3 }{ 4 }  of a revolution

(b)
 \frac { 3 }{ 4 }  of a revolution

(c) \frac { 1 }{ 2 }  of a revolution
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes 11

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
\left( \frac { 4 }{ 12 } \times 3 \right)  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
\left( \frac { 4 }{ 12 } \times 6 \right)  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
\left( \frac { 4 }{ 12 } \times 6 \right)  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
\left( \frac { 4 }{ 12 } \times 3 \right)  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
\left( \frac { 4 }{ 12 } \times 9 \right)  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
\left( \frac { 4 }{ 12 } \times 6 \right)  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.
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes 15

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.

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