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All questions of 3D Shapes for Grade 6 Exam

An angle whose measure is more than 90ο
  • a)
    acute angle
  • b)
    60º
  • c)
    obtuse angle
  • d)
    right angle
Correct answer is option 'C'. Can you explain this answer?

Shreshtha answered
Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees and less than 180 degrees
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In ∠PRQ, which of the following are the two arms?
  • a)
     
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Lavanya Menon answered
⇒ In ∠PRQ, Q is a vertex of an angle.
⇒ RP and RQ are two rays of an angle.
⇒ So, RP and RQ​ are two arms of ∠PRQ.

An angle whose measure is equal to one-fourth of a revolution is
  • a)
    right angle
  • b)
    straight angle
  • c)
    obtuse angle
  • d)
    acute angle
Correct answer is option 'A'. Can you explain this answer?

Prajnaloka Saha answered
Option 'A' is correct because...
Revolution = 360 degree
One fourth of revolution = 1X360/4
=90 degree
Since right angle is an angle whose measurement is 90 degree it is an right angle :)

How many metres is 805 cm?
  • a)
    80.5 m
  • b)
    8.5 m
  • c)
    8.50 m
  • d)
    8.05 m
Correct answer is option 'D'. Can you explain this answer?

Sanjeev answered
To convert 805 cm into metres:

1.Divide the number by 100. (805/100 because metre is equal to 100cm)

2.The result obtained is 8.05.

3.Then add the relative unit in the number to get the answer, which was 8.05m

Therefore option D is the correct answer.

An angle whose measure is equal to half of a revolution is
  • a)
    right angle
  • b)
    acute angle
  • c)
    straight angle
  • d)
    obtuse angle
Correct answer is option 'C'. Can you explain this answer?

Kunal Mehta answered
One full turn of the hand is 1 revolution. A right angle is 1/4 revolution and a straight angle is 1/2 a revolution. 
180 deg is considered as a straight line and half of the revolution is also 180 deg.

What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 7 to 10?
  • a)
    1/2
  • b)
    1/4
  • c)
    1/3
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Kalyan Sengupta answered
Answer:

To find the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 7 to 10, we need to determine the angle covered by the hour hand and express it as a fraction of a full revolution (360 degrees).

1. Calculate the angle covered by the hour hand in three hours:
- The hour hand moves 360 degrees in 12 hours since a clock completes one full revolution in 12 hours.
- Therefore, in one hour, the hour hand moves 360/12 = 30 degrees.
- In three hours, the hour hand would move 30 x 3 = 90 degrees.

2. Calculate the angle covered by a full revolution:
- A full revolution is 360 degrees.

3. Express the angle covered by the hour hand as a fraction of a full revolution:
- Fraction = Angle covered by the hour hand / Angle of a full revolution
- Fraction = 90/360
- Fraction = 1/4

Therefore, the fraction of a clockwise revolution that the hour hand of a clock turns through when it goes from 7 to 10 is 1/4, which corresponds to option 'B'.

Where will the hand of a clock stop if it starts at 12 and makes 3/4 of a revolution, clockwise?
  • a)
    6
  • b)
    9
  • c)
    3
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Mansi Yadav answered
•It's goes at 9

• We are at 12 and Move 3/4 revolution.

• So In first move we are at 3, then second move we are at 6, and then last move we are at 9.

• therefore the correct answer is 9 (B).

By what measure is the line m longer than the line n? 
  • a)
    1 cm
  • b)
    2 cm
  • c)
    3 cm
  • d)
    4 cm
Correct answer is option 'D'. Can you explain this answer?

Ashwani Mishra answered
Length of line A = 9 cm
Length of line B = 7−2 = 5 cm
Length of line A − length of line B = 9 − 5 = 4 cm
Hence, line A is 4 cm longer than line B.

Where will the hand of a clock stop if it starts at 2 and makes 1/4 of a revolution, clockwise?
  • a)
    5
  • b)
    11
  • c)
    8
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Krishna Patil answered
The correct answer is 5. As the starting point is 2, the 1/2 of it’s revolution will be at 8. Therefore it’s 1/4th will be at 5.

How is the measure of an angle expressed?
  • a)
    Compasses
  • b)
    Protractor
  • c)
    Degrees
  • d)
    Centimetres
Correct answer is option 'C'. Can you explain this answer?

Rounak Chawla answered
Measure of an angle

The measure of an angle is expressed in degrees. Degrees are a unit of measurement that is used to quantify the size of an angle. In geometry, angles are formed by two rays or line segments that share a common endpoint, called the vertex.

Degree measurement

The degree is a unit of measurement for angles, and it is denoted by the symbol °. A full circle is divided into 360 degrees. Each degree can be further divided into 60 minutes ('), and each minute can be divided into 60 seconds ("). These subdivisions are used for more precise measurements and are denoted by the symbols ' and " respectively.

Using a protractor

A protractor is a common tool used to measure and draw angles. It is a flat, semicircular instrument typically made of plastic or metal. The protractor is marked with a scale from 0 to 180 degrees, with each degree clearly labeled. To measure an angle with a protractor, you align the center point of the protractor with the vertex of the angle and then read the measure where the second ray or line segment intersects the protractor scale.

Alternative methods

While a protractor is a commonly used tool for measuring angles, there are alternative methods as well. Some compasses have a built-in protractor, allowing for both measuring and drawing of angles. Additionally, there are digital protractors available that provide a digital readout of the angle measurement.

Other units of angle measurement

While degrees are the most commonly used unit for measuring angles, there are other units as well. For example, radians are another unit used in trigonometry and calculus. In some specialized fields, such as surveying, grads (also known as gons or grades) may be used as a unit of angle measurement.

In conclusion, the measure of an angle is expressed in degrees, which is a unit of measurement. A protractor is a common tool used to measure angles, but there are also alternative methods available. Degrees are a widely accepted and standardized unit for measuring angles in geometry.

What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 1 to 10?
  • a)
    3/4
  • b)
    1/4
  • c)
    More than 3/4
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Debolina Shah answered
To solve this problem, we need to first understand the concept of a clockwise revolution and how it relates to the hour hand of a clock.

Clockwise revolution: A complete clockwise revolution is when the hour hand of a clock completes a full circle and returns to its starting position, which is 12 o'clock.

Hour hand: The hour hand of a clock represents the hours that have elapsed since the start of the day. It moves at a slower pace than the minute hand, which represents the minutes that have elapsed since the start of the hour.

Now, let's look at the question again. We need to find out what fraction of a clockwise revolution the hour hand of a clock turns through when it goes from 1 to 10. Here's how we can solve this problem:

Step 1: Determine the distance between 1 and 10 on a clock face.

We know that a clock face has 12 hour markers, so the distance between 1 and 10 is 9 hour markers.

Step 2: Calculate the angle between 1 and 10.

To calculate the angle between 1 and 10, we need to know that a full circle has 360 degrees. Since there are 12 hour markers on a clock face, each hour marker represents 30 degrees (360 degrees ÷ 12 hour markers = 30 degrees).

Therefore, the angle between 1 and 10 is:

9 hour markers × 30 degrees per hour marker = 270 degrees

Step 3: Determine what fraction of a clockwise revolution the hour hand turns through.

We know that a full clockwise revolution is 360 degrees, so we need to express 270 degrees as a fraction of 360 degrees.

270 degrees ÷ 360 degrees = 3/4

Therefore, the answer is 3/4, which means that the hour hand turns through 3/4 of a clockwise revolution when it goes from 1 to 10 on a clock face.

An angle which measures 0∘ is called a/an ___ angle.
  • a)
    zero
  • b)
    straight
  • c)
    obtuse
  • d)
    right
Correct answer is option 'A'. Can you explain this answer?

Rajat Chatterjee answered
Angle Measurement

An angle is formed when two lines or line segments meet at a common point. The measurement of an angle is based on the amount of rotation between the two lines, which is usually expressed in degrees.

Types of Angles

There are several types of angles based on their measurements. Let's briefly discuss them before addressing the specific question.

1. Zero Angle: An angle that measures 0 degrees is called a zero angle.
2. Acute Angle: An angle that measures less than 90 degrees is called an acute angle.
3. Right Angle: An angle that measures exactly 90 degrees is called a right angle.
4. Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees is called an obtuse angle.
5. Straight Angle: An angle that measures exactly 180 degrees is called a straight angle.
6. Reflex Angle: An angle that measures more than 180 degrees but less than 360 degrees is called a reflex angle.

The Zero Angle

A zero angle is a unique type of angle that measures 0 degrees. It can be visualized as two lines or line segments overlapping each other. Since there is no rotation or inclination between the lines, the angle formed is considered to be zero.

Why is the Answer 'A' - Zero Angle?

In the given question, it is stated that an angle measures 0. Based on the types of angles mentioned above, we can conclude that an angle measuring zero degrees is referred to as a zero angle. This means that the correct answer to the question is option 'A'.

It is crucial for students to understand the different types of angles and their measurements to solve geometry problems accurately. The concept of angles is extensively used in various mathematical and real-world applications, such as measuring distances, calculating areas, and determining shapes.

What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 5 to 11?
  • a)
    1/2
  • b)
    More than 1/4
  • c)
    3/4
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Shilpa Kulkarni answered
When it moves from 12 to 6, it moves two right angles, that is, 180�. This is 180/360 = � of one revolution. When the hour hand goes from 3 to 9, it moves or rotates by two right angles, that is 180�. When the hour hand of the clock goes from 4 to 7, it rotates by 1 right angle, that is 90�

l and m are two lines perpendicular to each other. What is the measure of the angle between them? 
  • a)
    10∘
  • b)
    50∘
  • c)
    40∘
  • d)
    90∘
Correct answer is option 'D'. Can you explain this answer?

Anirban Saini answered
Explanation:

When two lines are perpendicular to each other, they form a right angle. A right angle measures 90 degrees. Therefore, the measure of the angle between the two lines is 90 degrees.

Proof:

To prove that the angle between two perpendicular lines is 90 degrees, we can use the concept of alternate angles and the fact that the sum of angles in a straight line is 180 degrees.

1. Let's assume that line L is perpendicular to line M.
2. We can draw a transversal line that intersects both L and M.
3. When a transversal intersects two lines, it creates a pair of alternate angles.
4. Since L and M are perpendicular, the alternate angles created by the transversal will be congruent (equal in measure).
5. Let's label the alternate angles as angle 1 and angle 2.
6. Now, let's consider the straight line formed by line L, the transversal, and line M.
7. The sum of angles in a straight line is 180 degrees.
8. Therefore, angle 1 + angle 2 = 180 degrees.
9. Since angle 1 and angle 2 are congruent, we can rewrite the equation as 2 * angle 1 = 180 degrees.
10. Solving for angle 1, we get angle 1 = 90 degrees.
11. Hence, the measure of the angle between the perpendicular lines L and M is 90 degrees.

Conclusion:

The measure of the angle between two lines perpendicular to each other is always 90 degrees. Therefore, the correct answer is option D) 90.

What type of an angle is ∠AOB? 
  • a)
    An obtuse angle
  • b)
    A right angle
  • c)
    An acute tangle
  • d)
    A straight angle
Correct answer is option 'A'. Can you explain this answer?

Vp Classes answered
The angle ∠AOB shown in the image is an obtuse angle because it is greater than 90° but less than 180°.
Correct answer: a) An obtuse angle

Where will the hand of a clock stop if it starts at 3 and makes 1/2 of a revolution, clockwise?
  • a)
    9
  • b)
    5
  • c)
    6
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Sanskriti Sen answered
Explanation:

Starting Position:
- The hand of a clock starts at 3.

1/2 Revolution:
- A clock completes 1 full revolution in 12 hours.
- Therefore, 1/2 revolution will be equivalent to 6 hours.
- Starting from 3, if the hand moves clockwise for 6 hours, it will stop at 9.

Therefore, the hand of the clock will stop at 9 if it starts at 3 and makes 1/2 of a revolution clockwise. So, the correct answer is option 'A'.

What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from 12 to 9?
  • a)
    1/4
  • b)
    3/4
  • c)
    1/2
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Madhi Vadhani answered
When the hour hand of clock turn 3 right angles from 12 to 9.

3 right angles = 3/4

The fraction of clockwise revolution when it goes from 12 to 9 is 3/4

Where will the hand of a clock stop if it starts at 3 and makes 1/4 of a revolution, clockwise?
  • a)
    6
  • b)
    9
  • c)
    12
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Keerthana Menon answered
Explanation:
When a clock starts at 3 and makes 1/4 of a revolution clockwise, let's analyze what happens to the position of the hour hand.

1. The clock has 12 numbers (1 to 12) representing the hours.
2. A complete revolution of the hour hand takes 12 hours.
3. Thus, 1/4 of a revolution of the hour hand would take 12/4 = 3 hours.

Analysis:
1. The hour hand moves 3 hours clockwise from the starting position at 3.
2. Starting from 3, we count 3 hours clockwise, which leads us to the number 6 on the clock.

Conclusion:
Therefore, the hand of the clock will stop at the number 6 if it starts at 3 and makes 1/4 of a revolution clockwise. Hence, option 'A' is the correct answer.

Where will the hand of a clock stop if it starts at 6 and makes 3/4 of a revolution, clockwise?
  • a)
    12
  • b)
    9
  • c)
    6
  • d)
    3
Correct answer is option 'D'. Can you explain this answer?

Aishwarya Moopanar answered
A quarter of the clock is 3 hours. a full revolution is 12 hours. 3 quarters means 9 hours which means if we start the 3/4 revolution from 6 it would finish at 3. so it is the correct answer

Where will the hand of a clock stop if it starts at 2 and makes 1/2 of a revolution, clockwise?
  • a)
    5
  • b)
    8
  • c)
    11
  • d)
    None of these
Correct answer is option 'B'. Can you explain this answer?

Arindam Saha answered
Explanation:

To solve this problem, we need to understand how a clock works and how the hands move.

Understanding the Clock:

A clock has two hands - an hour hand and a minute hand. The hour hand is shorter and moves slowly, while the minute hand is longer and moves faster. The hour hand completes one full revolution in 12 hours, while the minute hand completes one full revolution in 60 minutes.

The Starting Point:

The problem states that the clock hand starts at 2. This means that the hour hand will be pointing towards the 2 on the clock face, and the minute hand will be pointing towards the 12.

Making 1/2 Revolution:

The problem also states that the hand makes 1/2 of a revolution clockwise. This means that the hand will move in the direction of the numbers on the clock face and cover half the distance between its starting point and its ending point.

Determining the Ending Point:

To determine where the hand will stop, we need to determine the fraction of the clock that represents 1/2 of a revolution. Since a clock has 12 numbers, 1/2 of a revolution will cover 6 numbers.

Starting from 2, if we move clockwise and cover 6 numbers, we will end up at 8. Therefore, the hand will stop at 8.

Answer:

The hand of the clock will stop at 8.

How do we write  is perpendicular to '' symbolically?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Get Idea answered
To express that one vector is perpendicular to another, simply place the symbol ⊥ between the two vectors.

Where will the hand of a clock stop if it starts at 12 and makes 1/2 of a revolution, clockwise?
  • a)
    6
  • b)
    9
  • c)
    3C
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

EduRev CAT answered
Explanation:


  • Starting Position: The clock hand starts at 12.

  • Half of a Revolution: Half of a revolution on a clock is equal to 6 hours.

  • Direction: The question specifies that the hand moves clockwise.

  • Final Position: Therefore, the hand will stop at 6.

How many pairs of parallel lines are there in the given figure?  
  • a)
    2
  • b)
    1
  • c)
    4
  • d)
    3
Correct answer is option 'A'. Can you explain this answer?

Get Idea answered
The opposite sides of the rectangle are parallel to each other. There are two such pairs of sides:
  • The two horizontal sides are parallel to each other.
  • The two vertical sides are parallel to each other.
Thus, there are 2 pairs of parallel lines in a rectangle.
The correct answer is: a) 2.

Which is the longest rectangle ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Devika Nair answered
By observing & comparing the given figures, rectangle B is the longest rectangle.

At 5:20 what type of angle is formed between the two hands of a clock?
  • a)
    An obtuse angle
  • b)
    A right angle
  • c)
    An acute angle
  • d)
    A reflex angle
Correct answer is option 'C'. Can you explain this answer?

Get Idea answered
  • The minute hand at 20 minutes points to the 4 on the clock.
  • The hour hand at 5:20 is slightly past the 5. Each hour mark represents 30 degrees (360 degrees/12 hours).
  • The angle between 5 and 4 is 30 degrees per hour mark, hence 30 + 10 = 40 degrees.
  • A 40-degree angle is acute, making the correct answer C: An acute angle.

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