# Free Understanding Elementary Shapes Subjective Test 02 Practice Test - 6th grade

### Question 1

Given line segments of lengths AB= 5 m, BC = 4 m, AC = 9m, which of the points lie between the other two? [1 MARK]

#### SOLUTION

Solution :

Given that

The length of the line segment AB = 5m

The length of the line segment BC = 4m

The length of the line segment AC = 9m

The length of AB+BC = 9m = AC

According to the given conditions, AB + BC = AC. So, B lies in between A and C.

### Question 2

What fraction of a clockwise revolution does the hour hand of a clock turns through:

a) when it moves from 3 to 8?

b) when it moves from 3 to 9?

[2 MARKS]

#### SOLUTION

Solution :Each option: 1 Mark

When the hour hand completes one complete revolution it completes 360 degrees.a) When the hour hand moves from 3 to 6 it covers 90 degrees. When it moves from 6 to 8 it covers 60 degrees. So, the angle covered when hour hand moves from 3 to 8 is 150 degrees.

Fraction that it has moved = 150360 = 512

b) When the hour hand of the clock moves from 3 to 9 it moves through two right angles.

So the angle it covers when it moves from 3 to 9 = 180 ∘

Fraction that it has moved = 180360 = 12

### Question 3

What is the measure of an angle:

a) less than a right angle called?

b) greater than a right angle called?

[2 MARKS]

#### SOLUTION

Solution :Each Point: 1 Mark

We know that a right angle is equal to 90∘

a) Any angle less than a right angle is an acute angle.

b) If an angle is greater than 90∘ and less than 180∘, then it is called an obtuse angle.

If an angle is greater than 180∘ then it is called a reflex angle.

### Question 4

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]

#### SOLUTION

Solution :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.

### Question 5

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]

#### SOLUTION

Solution :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 6

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?

[3 MARKS]

#### SOLUTION

Solution :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.

### Question 7

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]

#### SOLUTION

Solution :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 8

What is the shape of the following objects:

(a) A sweet laddu

(b) A road-roller

(c) A Matchbox

(d) A brick

[4 MARKS]

#### SOLUTION

Solution :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 9

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]

#### SOLUTION

Solution :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 10

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.

[4 MARKS]

#### SOLUTION

Solution :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.