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Cubes and Cube Roots

    Extra Curriculum Support

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8th class > Cubes and Cube Roots > Extra Curriculum Support

Extra Curriculum Support

This is a comprehensive educational resource designed to provide students with the tools and guidance necessary to excel. This support system is structured to cater to various aspects of learning, ensuring that students are well-prepared for academic challenges and practical applications of mathematical concepts. Some are the key benefits are mentioned below:

1.Comprehensive Learning: This holistic approach helps students gain a thorough understanding of the subject. Practical Application: The resources encourage students to apply mathematical concepts to real-life scenarios, enhancing their practical understanding and problem-solving skills.

2.Critical Thinking and Reasoning: Value-Based and HOTS questions promote critical thinking and reasoning abilities. These skills are crucial for students to tackle complex problems and make informed decisions.

3.Exam Preparedness: Sample Question Papers and NCERT Exemplar Solutions provide ample practice for exams. They help students familiarize themselves with the exam format and types of questions, reducing exam anxiety.

4.Ethical and Moral Development: Value-Based Questions integrate ethical and moral lessons into the learning process, helping in the overall development of students' character and social responsibility. By incorporating these diverse elements, Enhanced Curriculum Support aims to provide a robust and well-rounded knowledge, preparing students for both academic success and real-world challenges.

Sample Question Papers

About this Section

Sec A

  1. The smallest number which when multiplied with 7200 will make the product a perfect cube, is:

(a) 30 (b) 15 (c) 10 (d) 20

  1. Which of the following numbers is not a perfect cube?

(a) 343 (b) 567 (c) 125 (d)216

  1. The cube root of −3431331 is:

(a) 117 (b) −117 (c) −711 (d) 711

  1. By which smallest natural number should 135 be divided so that the quotient is a perfect cube?

(a) 2 (b) 3 (c) 9 (d) 5

  1. If the volume of a cubical box is 35.937 m3, what is the length of its one side?

(a) 6.3 m (b) 6.6 m (c) 3.3 m (d) 3.6 m

  1. Find the smallest number by which the number 100 must be multiplied to obtain a perfect cube.

(a) 4 (b) 2 (c) 10 (d) 5

  1. The unit’s digit of the cube of a number is 9. The unit’s digit of its cube root is:

(a) 1 (b) 3 (c) 7 (d) 9

  1. The number of Zeroes at the end of the cube of the number 20 is:

(a) 2 (b) 3 (c) 6 (d) 1

  1. In the five digit number 1b6a3, a is the greatest single digit perfect cube and twice of it exceeds b by 7. Then the sum of the number and its cube root is:

(a) 19710 (b) 18700 (c) 11862 (d) 25320

  1. The product 864 × n is a perfect cube. What is the smallest possible value of n?

(a) 3 (b) 4 (c) 1 (d) 2

  1. By which smallest natural number should 128 be divided so that the quotient is a perfect cube?

(a) 6 (b) 4 (c) 3 (d) 2

Sec B

  1. Find out if 6859 is a perfect cube?

  2. Using prime factorisation, find the cube root of 2197.

  3. Using prime factorization, show that 729 is a perfect cube.

  4. Find if 15625 is a perfect cube?

Value Based Questions

About this Section

Problem 1

  1. A community center is organizing a toy donation drive. They aim to donate small wooden cubes to children in need. If each donated box contains 8 wooden cubes, and the center donates 100 boxes, how many individual cubes are donated? Reflect on how this small gesture can positively impact the lives of children in need.

Problem 2

  1. A construction company uses cubical blocks to build low-cost houses for underprivileged families. If they need to ensure that the volume of the blocks used is minimized to save resources, how should they determine the side length of the cubes? Discuss the importance of resource management in sustainable development.

Problem 3

  1. A gym is designed with cubical storage spaces for keeping the members' belongings. If each storage space has a side length of 2 meters, calculate the volume of each storage space. Discuss the role of organized and spacious environments in promoting mental well-being and a healthy lifestyle.

HOTS

About this Section

Q1

  1. Compare the growth rates of squares and cubes. For which values of n does the cube of n exceed the square of n by at least 1000? Formulate and solve an equation to find these values.

Q2

  1. If the sum of the cubes of three consecutive natural numbers is equal to the cube of a fourth number, find the relationship between these four numbers. Prove your answer.

Q3

  1. A cube of side 5 cm is melted and recast into smaller cubes each with a side of 1 cm. How many smaller cubes are formed? If you were to assemble these smaller cubes back into a large cube, what would be the side length of the new cube?

Q4

  1. Consider a number x such that x3 = 29. Without directly calculating x, express x as a power of 2 and explain your reasoning.

NCERT Exemplar Solutions

About this Section

Choose the correct option

Questions

  1. The one’s digit of the cube of 23 is:

(a) 6 (b) 7 (c) 3 (d) 9

  1. Which of the following numbers is a perfect cube?

(a) 243 (b) 216 (c) 392 (d) 8640

  1. Which of the following numbers is not a perfect cube?

(a) 216 (b) 567 (c) 125 (d) 343

Fill in the blanks

Questions

  1. The cube of 0.3 is ?

  2. The cube of 100 will have ? zeroes.

  3. There are ? perfect cubes between 1 and 1000.

  4. The cube of an odd number is always an ? number.

  5. Ones digit in the cube of 38 is ?

  6. The least number by which 72 be multiplied to make it a perfect cube is ?

  7. The least number by which 72 be divided to make it a perfect cube is ?

  8. Cube of a number ending in 7 will end in the digit ?

State whether the given statements are True/False.

Questions

  1. If a2 ends in 9, then a3 ends in 7.

  2. The cube root of 8000 is 200.

  3. The cube of 0.4 is 0.064.

  4. The cube of a one digit number cannot be a two digit number.

  5. Cube of an even number is odd.

  6. Cube of an odd number is even.

  7. Cube of an even number is even.

  8. Cube of an odd number is odd.

  9. There is no cube root of a negative integer.

Answer the below given questions.

Questions

  1. Using prime factorisation, find the cube root of 5832.

  2. Is 9720 a perfect cube? If not, find the smallest number by which it should be divided to get a perfect cube.

  3. Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.

  4. Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. Find the numbers.

  5. 52+122123 = ?

  6. 62+82123 = ?

Case Based Questions

About this Section

Q1

  1. A warehouse manager needs to store cubic crates of goods. Each crate has a side length of 1 meter. The warehouse has a cubic storage room with a side length of 10 meters. The manager wants to utilize the storage room to its maximum capacity.

How many cubic crates can the manager store in the warehouse?

If the manager decides to stack the crates such that the height of the stack is half the height of the storage room, how many crates can be stored in the room now?

Discuss the practical considerations the manager should keep in mind to avoid overloading the storage space and ensuring easy access to all crates.

Q2

  1. A city planner is designing a small park that will feature a cubical water fountain at its center. The fountain has a side length of 2 meters, and the park is designed such that the fountain is surrounded by a square lawn. The planner wants the area of the lawn to be four times the area occupied by the fountain.

Calculate the area occupied by the fountain.

What will be the side length of the square lawn surrounding the fountain?

How does incorporating natural elements like a water fountain and lawn into urban design contribute to environmental sustainability and the well-being of the community?