Samacheer Kalvi Class 8 Maths Solutions Chapter 2 Measurements InText Questions

Think (Text Book Page No. 51)

Question 1. \( \frac{22}{7} \) and 3.14 are rational numbers. Is ' \( \pi \) ' a rational number? Why?
Answer: The numbers \( \frac{22}{7} \) and 3.14 are rational because they can be written as a simple fraction or a terminating/repeating decimal. For example, 3.14 can be written as \( \frac{314}{100} \). However, the number \( \pi \) (pi) is not a rational number. This is because its decimal expansion goes on forever without repeating any pattern. This makes \( \pi \) an irrational number.
In simple words: \( \frac{22}{7} \) and 3.14 are rational numbers as they can be written as simple fractions. But \( \pi \) is irrational because its decimal part never ends and never repeats in a pattern.

🎯 Exam Tip: Remember the key difference: rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot.

Question 2. When is the ' \( \pi \) ' day celebrated? Why?
Answer: Pi Day is celebrated every year on March 14th. This specific date (3/14 in the American date format) is chosen because the first three digits of pi are 3.14. It's a fun way to recognize and celebrate the mathematical constant \( \pi \), which is essential in geometry and physics.
In simple words: Pi Day happens on March 14th each year. This is because the number pi starts with 3.14.

🎯 Exam Tip: Knowing famous mathematical constants and their related dates can be a fun way to remember key facts. Pi is used for finding the circumference and area of circles.

Think (Text Book Page No. 53)

Question. The given circular figure is divided into six equal parts. Can we call the parts as sectors? Why?
Answer: No, these equal parts are not considered sectors. A true sector of a circle is a flat area bounded by two straight lines (radii) coming from the center, and a curved edge (an arc) of the circle. In this figure, the boundaries of the parts are not straight radii, which means they do not originate from the center of the circle to the circumference. Therefore, they do not fit the definition of a sector.
In simple words: No, these parts are not sectors. Sectors have straight sides (radii) that start from the center of the circle, but these parts do not have those straight sides.

🎯 Exam Tip: Clearly define geometrical terms. A sector is like a slice of pizza, defined by two radii and an arc, while a segment is bounded by a chord and an arc.

Try These (Text Book Page No. 53)

Question. Fill the central angle of the shaded sector (each circle is divided into equal sectors)
Answer: To find the central angle of each shaded sector, we divide the total angle of a circle (360°) by the number of equal parts (n) the circle is divided into. The formula used is: Central angle \( = \frac{360^\circ}{n} \). This calculation helps determine the exact angular size of each identical slice of the circle.

Sector

Central angle

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