Olympiad Test: Understanding Elementary Shapes - Class 6 MCQ

1 meter (m) is equal to 100 centimeters (cm).

To convert 3 meters to centimeters:

• Multiply: 3 × 100 = 300

Therefore, 3 meters is equal to 300 centimeters.

Solution:

To convert 805 cm into metres, follow these steps:

• Understand that 100 cm equals 1 m.
• Thus, 1 cm is equal to 1/100 m.
• To find the value in metres, divide 805 cm by 100:
• 805 cm in metres = 805/100 m.

The formula used is simple: divide the length by 100.

The correct conversion gives you 8.05 m.

Solution:

To find the length of the string, we can break it down into segments:

• Calculate the distance from point A to point B: (4.5 - 2.5)
• Calculate the distance from point A to point C: (4.5 - 3.0)
• Calculate the distance from point C to point D: (7.5 - 3.5)

Now, we can add these distances together:

• First segment: 2 cm
• Second segment: 1.5 cm
• Third segment: 4 cm

Adding these values gives:

2 + 1.5 + 4 = 7.5 cm

This approximates to 8 cm.

By observing and comparing the given figures, we can conclude that:

• Rectangle B is the longest rectangle.
• Visual comparison shows that B has the greatest length among the options.
• This method is straightforward and effective for identifying the longest rectangle.

An angle which measures more than 0° and less than 90° is called an acute angle.

• Acute Angle: Measures between 0° and 90°.
• Obtuse Angle: Measures between 90° and 180°.
• Right Angle: Measures exactly 90°.
• Straight Angle:  Measures exactly 180°.

Therefore, the correct answer is B: Acute angle.

The measure of an angle is expressed in degrees. To measure angles accurately, we use a protractor. Here are some key points about angle measurement:

• One complete revolution is divided into 360 degrees.
• Each degree is a part of this division, written as 360°.
• A right angle measures 90°.
• A straight angle measures 180°.
• An acute angle is less than 90°.
• An obtuse angle is greater than 90° but less than 180°.
• A reflex angle is greater than 180°.

To measure an angle using a protractor:

• Align the midpoint of the protractor with the vertex of the angle.
• Ensure one ray of the angle aligns with the 0° mark on the protractor.
• Read the degree measurement where the other ray intersects the curved edge.

For example, if the measurement is 40°, we write it as m∠ABC = 40°.

Length of line A = 9 cm

Length of line B = 7 - 2 = 5 cm

The difference in length is calculated as follows:

• Length of line A - Length of line B = 9 - 5 = 4 cm

Thus, line A is 4 cm longer than line B.

An angle that measures 0° is called a zero angle because there is no separation between the two rays that form the angle.

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

A straight angle measures exactly 180°.

• It forms a straight line, appearing flat without any bend.
• Unlike a zero angle (0°), right angle (90°), or acute angle (less than 90°), the straight angle uniquely represents a half-turn.
• This makes it distinct in geometry for creating straight lines and forming linear pairs with other angles.

• 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.

• Perpendicular Lines Defined: When two lines are perpendicular, they intersect at a right angle.
• Right Angle Measurement: A right angle always measures exactly 90 degrees.
• Application to Lines l and m: Since lines l and m are perpendicular, the angle between them is 90°.

Therefore, the correct measure of the angle between lines l and m is 90°.

179° is classified as an obtuse angle because:

• An angle is considered obtuse if it is greater than 90° but less than 180°.
• Since 179° is greater than 90° and less than 180°, it falls within this range.

Therefore, 179° is indeed an obtuse angle.

An angle measuring less than 90° is known as an acute angle. Since 89° is less than 90°, it qualifies as an acute angle.

When an arm of an angle is extended, the measure of the angle remains the same. The angle itself does not change; only the position of one of its arms is altered. The extension does not affect the measurement of the angle.

Reflex angles are those that "bend back" on themselves, creating an angle larger than a straight line (180°) but less than a full circle (360°). Therefore, the angle of 270° fits this definition.

Key points about reflex angles:

• A reflex angle is greater than 180°.
• It is less than 360°.
• 270° is a classic example of a reflex angle.

Thus, the correct answer is 270°.

⇒ 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.

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

The lines that lie on the same plane and do not intersect at any point are called parallel lines. They have the following characteristics:

• They maintain a constant distance apart.
• They will never meet, regardless of how far they are extended.

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.