Ncert Solutions For Class 8 Maths Chapter 11 Try These

NCERT Solutions for Class 8 Maths Chapter 11 Try These

Mensuration is a fundamental branch of mathematics that deals with the measurement of geometric figures and their parameters like area, perimeter, volume, and surface area. In the NCERT Class 8 Maths textbook, Chapter 11 focuses extensively on these concepts, providing students with a comprehensive understanding of how to measure various two-dimensional and three-dimensional shapes. The "Try These" exercises in this chapter are particularly valuable as they encourage students to apply theoretical knowledge to practical problems, reinforcing their learning through hands-on practice.

Overview of Chapter 11 Mensuration

Chapter 11 in the NCERT Class 8 Maths curriculum covers several crucial topics including:

• Area of trapezium, general quadrilaterals, and polygons
• Area of a circle
• Surface area of cube, cuboid, and cylinder
• Volume of cube, cuboid, and cylinder
• Volume and capacity

The "Try These" sections interspersed throughout the chapter are designed to help students verify concepts, explore properties, and apply formulas in different contexts. These exercises bridge the gap between theory and application, making abstract mathematical concepts more concrete and understandable.

Detailed Solutions for "Try These" Exercises

Exercise 11.1: Area of Trapezium

Try These (Page 170):

1. Find the area of a rhombus whose diagonals are 10 cm and 8 cm.

Solution: The area of a rhombus can be calculated using the formula: Area = (d₁ × d₂) ÷ 2 Where d₁ and d₂ are the lengths of the diagonals.

Given: d₁ = 10 cm d₂ = 8 cm

Area = (10 × 8) ÷ 2 Area = 80 ÷ 2 Area = 40 cm²

2. The area of a trapezium-shaped field is 480 m². The distance between the two parallel sides is 15 m and one of the parallel sides is 20 m. Find the other parallel side.

Solution: The area of a trapezium is given by: Area = (sum of parallel sides × height) ÷ 2

Given: Area = 480 m² Height = 15 m One parallel side = 20 m Let the other parallel side be x.

480 = ((20 + x) × 15) ÷ 2 960 = (20 + x) × 15 960 ÷ 15 = 20 + x 64 = 20 + x x = 64 - 20 x = 44 m

Exercise 11.2: Area of a Circle

Try These (Page 177):

1. The circumference of a circle is 31.4 cm. Find its radius and area.

Solution: Given: Circumference = 31.4 cm

We know that: Circumference = 2πr 31.4 = 2 × (22/7) × r 31.4 = (44/7) × r r = 31.4 × 7 ÷ 44 r = 4.99 cm ≈ 5 cm

Now, to find the area: Area = πr² Area = (22/7) × 5² Area = (22/7) × 25 Area = 550/7 Area ≈ 78.57 cm²

2. Find the area of a circle whose diameter is 14 cm.

Solution: Given: Diameter = 14 cm Radius = Diameter ÷ 2 = 14 ÷ 2 = 7 cm

Area = πr² Area = (22/7) × 7² Area = (22/7) × 49 Area = 22 × 7 Area = 154 cm²

Exercise 11.3: Surface Area and Volume

Try These (Page 186):

1. Find the total surface area of a cuboid whose length, breadth, and height are 20 cm, 15 cm, and 10 cm respectively.

Solution: Given: Length (l) = 20 cm Breadth (b) = 15 cm Height (h) = 10 cm

Total Surface Area of cuboid = 2(lb + bh + hl) = 2[(20 × 15) + (15 × 10) + (10 × 20)] = 2[300 + 150 + 200] = 2 × 650 = 1300 cm²

2. Find the volume of a cylinder whose base area is 180 cm² and height is 15 cm.

Solution: Given: Base Area = 180 cm² Height = 15 cm

Volume of cylinder = Base Area × Height = 180 × 15 = 2700 cm³

Benefits of Working Through "Try These" Exercises

The "Try These" exercises in NCERT Class 8 Maths Chapter 11 offer several significant benefits:

1. Conceptual Reinforcement: These exercises help students verify and reinforce the concepts they've learned in the chapter.

2. Application Skills: They develop students' ability to apply formulas and concepts to solve different types of problems.

3. Critical Thinking: Many "Try These" questions encourage students to think beyond the textbook and explore various approaches to solutions.

4. Error Identification: By working through these exercises, students can identify common mistakes and learn to avoid them.

5. Confidence Building: Successfully solving these problems builds confidence in tackling more complex mensuration problems.

Tips for Mastering Mensuration Concepts

To excel in mensuration and make the most of the "Try These" exercises, consider these strategies:

1. Understand Formulas, Don't Just Memorize: Focus on understanding how formulas are derived rather than simply memorizing them.

2. Draw Diagrams: Visualizing problems by drawing accurate diagrams helps in better understanding and solving.

3. Practice Regularly: Consistent practice with different types of problems builds familiarity and speed.

4. Create Formula Cards: Make flashcards with important formulas and review them regularly.

5. Real-world Connections: Try to relate mensuration problems to real-life situations to make learning more

Real-world Connections: Try to relate mensuration problems to real-life situations to make learning more engaging and relevant. For instance, calculating the paint required for a room or the volume of water in a tank helps students see the practical value of these concepts.

Final Thoughts: Embracing the Challenge

The "Try These" exercises in NCERT Class 8 Maths Chapter 11 are not just additional problems—they are opportunities to deepen understanding and build resilience. By tackling these questions, students move beyond rote learning and develop the analytical skills necessary to approach unfamiliar problems with confidence. Whether it’s calculating the area of a circle or the volume of a cylinder, each exercise reinforces the idea that mathematics is a dynamic tool for solving everyday challenges.

In conclusion, mastering mensuration requires a blend of conceptual clarity, consistent practice, and curiosity. The exercises and tips outlined here serve as a roadmap for students to navigate the complexities of geometry, ensuring they are well-prepared for higher-level mathematics and real-world applications. Remember, every problem solved is a step toward mathematical proficiency and lifelong problem-solving skills.

Beyond theexercises themselves, students can amplify their learning by weaving mensuration into broader mathematical narratives.

Connecting with Algebra and Trigonometry – When a problem asks for the height of a ladder leaning against a wall, it opens a gateway to algebraic equations and, eventually, to trigonometric ratios. By recognizing these links, learners see how geometry is not an isolated chapter but a thread that runs through the entire syllabus.

Leveraging Technology – Interactive apps and geometry software let students manipulate three‑dimensional shapes in real time. Visualizing a solid as it is sliced or rotated deepens spatial intuition far more quickly than static textbook diagrams.

Collaborative Problem‑Solving – Forming study groups to discuss “Try These” questions encourages diverse perspectives. Explaining a solution to peers reinforces one’s own understanding and uncovers alternative strategies that might not surface during solitary practice.

Assessing Mastery – Periodic self‑quizzes that mimic exam‑style questions help students gauge their readiness. Timing these attempts builds the speed and accuracy needed for classroom tests and competitive examinations alike.

Cultivating a Growth Mindset – When a problem feels daunting, treating it as a puzzle rather than a roadblock transforms anxiety into curiosity. Celebrating small victories—such as correctly identifying the radius of a circle after a misstep—reinforces the belief that effort leads to improvement.

Looking Ahead – Mastery of Class 8 mensuration sets a sturdy foundation for the more abstract concepts that await in higher grades, such as surface area of composite solids, volume of irregular figures, and the introduction of coordinate geometry. By internalizing the principles outlined here, students will approach those future topics with confidence, ready to translate everyday observations into precise mathematical language.

In summary, the journey through mensuration is more than a chapter in a textbook; it is a stepping stone toward analytical thinking, practical problem‑solving, and a lifelong appreciation for the patterns that shape our world. Embracing the challenges it presents equips learners not only with the tools to excel academically but also with the mindset to tackle real‑life complexities with clarity and creativity.