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6th Grade > Mathematics

UNDERSTANDING ELEMENTARY SHAPES MCQs

Total Questions : 97 | Page 9 of 10 pages
Question 81.


If the minute hand of a clock sweeps an arc from 4 to 6 , find the angle through which it has rotated and the type of triangle formed. [3 MARKS]


 Discuss Question
Answer: Option A. ->
:

Visualisation: 1 Mark
Finding the angle: 1 Mark
Type of Triangle: 1 Mark
The minute hand covers an angle of 30 in every five minutes. The angle covered in moving from 4 to 6 is 60.
The length of the minute hand remains constant. So the two sides of the triangle will be equal. 
So the angles will be same for the sides which are equal.
Now, the angle included between the sides whose length are equal is 60.
So the other angles are (180-60)÷2 = 60.
Hence all the angles of the triangle are 60.
The the triangle formed is an equilateral triangle.


If The Minute Hand Of A Clock Sweeps An Arc From 4 To 6 , Fi...


Question 82.


Given in a clock, the hour hand is fixed at 12 and the minute hand is made to rotate. The reading of the angle moved by minute hand is taken as twice its actual reading. If the minute hand is at 6 according to the wrong reading, what is the position of minute hand according to the actual reading? Also, find the actual angle rotated by the minute hand. [4 MARKS]


 Discuss Question
Answer: Option A. ->
:

Steps: 2 Marks
Actual Reading: 1 Mark
Angle Rotated: 1 Mark
The minute hand when points at 6 cover an angle of 180 degrees.

As per question reading of the minute hand moved is twice the actual reading.
So, it will be pointing at 3.


Now for every five minutes, the minute hand would rotate through 30.
So when the minute hand passes from 12 to 3, total minutes passed =15.
Therefore the actual angle rotated by the minute hand = 3×30 = 90


Question 83.


What is the shape of the following objects:
(a) A sweet laddu
(b) A road-roller
(c) A Matchbox
(d) A brick
[4 MARKS]


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Answer: Option A. ->
:
Each option: 1 Mark
(a) A sweet laddu is Spherical in shape.
(b)A road-roller is Cylindrical in shape.
(c)A Matchbox is in the shape of a  Cuboid.
(d) A brick is in the shape of a Cuboid.
 
Question 84.


A football ground is in the shape of a rectangle. The ends of the centre line (EF) and the midpoints of the end lines (AB and CD) are joined to form a quadrilateral. Find the angle between the diagonals of the quadrilateral so formed?


A Football Ground Is In The Shape Of A Rectangle. The Ends ...
[3 MARKS] 


 Discuss Question
Answer: Option A. ->
:

Steps: 2 Marks
Answer: 1 Mark
Given that:
ABCD is a rectangle.
E and F are the mid-points of the lines AC and BD respectively.
AE=BF=EC=FD
Also, AH=HB=CG=GD   [ H is mid point of AB , G is midpoint of CD ]
A, B, C and D are right angles.
The four sides of  rectangle formed i.e. EHFG will have equal dimensions. 
The length of all their diagonals will also be same.
EH=HF=FG=EG
All sides of the quadrilateral are equal.
So either it will be a Rhombus or a Square.
But for both of these quadrilaterals, the diagonals intersect at a right angle.
 The angle formed between the diagonals is a right angle.


A Football Ground Is In The Shape Of A Rectangle. The Ends ...


Question 85.


Given the sides of a quadrilateral are of equal length and each of its angles measures the same which is when the minute hand moves from 3 to 6. Find the angle between the diagonals. [3 MARKS]


 Discuss Question
Answer: Option A. ->
:

Steps: 2 Marks
Answer: 1 Mark
The angle covered when the minute hand moves from 3 to 6 is 90 degrees.


Given that:
The sides of the quadrilateral are equal.
So the quadrilateral can either be a rhombus or a Square.
But the angles included between the sides is 90.
The quadrilateral is a Square.
Now in a square, the diagonals intersect each other at 90.
So angle between the diagonals is 90


Question 86.


What is a line segment? How is it different from a line?
a. In fig how many points are marked? Name them.

b. In fig how many line segments are there? Name them.
What Is A Line segment? How Is It different from A Line?a...
[4 MARKS]


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Answer: Option A. ->
:
Definition: 1 Mark
Difference: 1 Mark
Each Point: 1 Mark
A line segment is a line which is contained between two points. The length of the line segment is fixed.
While a line has no ends and it is denoted with an arrow at both the ends.
a. In the given figure five points A, B, C, D, and E are marked.

b. In the given figure there are ten line segments AB, AD, AE, AC, BD, BE, BC, DE, DC and EC.
Question 87.


Name the following types of triangles:
a)Triangle with length 9m, 9m, 9m
b)Triangle with length 6m, 6m, 9m
c)Triangle with angles 90, 40, 50
d)Triangle with angles 70, 70, 40
[4 MARKS]


 Discuss Question
Answer: Option A. ->
:
Solutions: 1 Mark each
a) The length of all sides of the triangle is equal.
So it is an equilateral triangle.
b) In this triangle two sides are=6m
So it is an isosceles triangle.
c) In this triangle one of the angles is 90, so the triangle is a right-angled triangle.
d) In this triangle, two angles are equal to 70.So it is an isosceles triangle.
Question 88.


A ball is thrown from point A and it reaches point B which is 7m away. There is another point C which lies somewhere on the line AB. Given that the ball follows a straight path, and AC = 9m, BC = 2m. Which is the point that lies in between  other two? Draw the path of the ball. [1 MARK]


 Discuss Question
Answer: Option A. ->
:


Given that
Length of line AB = 7m
Length of line AC = 9m
Length of line BC = 2m
We can clearly see that the length of line AC > BC.
Also, AB + BC = AC
 Point B lies between A and C.  


 AB + BC = AC.


A Ball Is Thrown From point A And It Reaches point B Which...


Question 89.


What fraction of a clockwise revolution does the hour hand turn through when it rotates from: [2 MARKS]
a) 3 to 6
b) 6 to 12


 Discuss Question
Answer: Option A. ->
:
Fractions: 1 Mark each
We may observe that in one complete clockwise revolution, the hour hand will rotate through 360
a) We have to find out the fraction of a clockwise revolution that an hour hand turns through when it rotates from 3 to 6.
Now, when the hour hand rotates from 3 to 6 it will rotate through 1 right angle. 
The fraction of revolution = 90360 = 14 revolution
b) Here the hour hand rotates from 6 to 12, which is to right angles.
The fraction of revolution = 180360 = 12 revolution
Question 90.


Given a ABC, and the sum of two angles of the triangle is 90. What type of triangle is it? [2 MARKS]


 Discuss Question
Answer: Option A. ->
:

Triangle: 2 Marks
Given that:
The sum of two angles of the triangle is 90
.
We know that the sum of all the three angles in a triangle is 180.
The other angle = 180-90 = 90
Now we know that if one of the angles in a triangle is 90, then the triangle is a right-angled triangle.
Hence, the given triangle is a right-angled triangle.


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