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.
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
2. Which of the following numbers is not a perfect cube?
(a) 343 (b) 567 (c) 125 (d)216
3. The cube root of
(a)
4. 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
5. 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
6. 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
7. 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
8. The number of Zeroes at the end of the cube of the number 20 is:
(a) 2 (b) 3 (c) 6 (d) 1
9. 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
10. The product 864 × n is a perfect cube. What is the smallest possible value of n?
(a) 3 (b) 4 (c) 1 (d) 2
11. 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?
5. Verify whether 512 is a perfect cube or not using the prime factorization method.
6. Write the cubes of the first five natural numbers.
7. Find the smallest number that must be multiplied with 81 to make it a perfect cube.
SecC
1. Find the cube root of 13824 using the prime factorization method.
2. The volume of a cubical box is 512 cm³. Find the length of its side.
3. Verify whether 3375 is a perfect cube. If yes, find its cube root using prime factorization.
4. A number is formed by multiplying
5. The volume of a cube increases from 343 m³ to 729 m³. By what percentage has the side length of the cube increased?
6. A cube-shaped container has a volume of 1000 cm³. How much surface area will be exposed if the container is open from the top?
7. Find the smallest number that must be subtracted from 129 to make it a perfect cube. Also, find the cube root of the resulting number.
8. A factory manufactures spherical balls of diameter 6 cm by melting a cubical block of iron with a side of 12 cm. How many balls can be made from one block?
SecD
1. A wooden cube has a volume of 3375 cm³. The cube is painted on all six faces and then cut into smaller cubes, each with a volume of 125 cm³. Find:
(a) The total number of smaller cubes formed.
(b) The number of smaller cubes with no painted faces.
2. A sugar cube with a side length of 1 cm is packed into a larger cubical box with a side length of 10 cm. How many sugar cubes can fit into the larger box?
3. A cubical tank can hold 1728 liters of water. Find the length of its side. If the tank is lined with tiles at a cost of ₹5 per square meter, calculate the total cost for tiling the inner surface.
4. If the sum of the cubes of three consecutive integers is 855, find the integers.
5. A metal cube with a side of 12 cm is melted and recast into smaller cubes with a side of 4 cm. How many smaller cubes can be formed? If 20% of the smaller cubes are defective, how many usable cubes remain?
6. A perfect cube number has its cube root equal to the sum of three consecutive integers. Find the cube and its cube root.
Problem 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
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
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.
Q1
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
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
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
Consider a number x such that
Choose the correct option
Questions
1. The one’s digit of the cube of 23 is:
(a) 6 (b) 7 (c) 3 (d) 9
2. Which of the following numbers is a perfect cube?
(a) 243 (b) 216 (c) 392 (d) 8640
3. 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
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.
6.
Q1
A company has a warehouse with a cubic storage space. The warehouse is designed to store large items, and the manager needs to store crates that are shaped like cubes. Each crate is made of metal and is in the shape of a perfect cube, with each side measuring 8 meters.
The company wants to optimize the use of space in the warehouse by stacking these crates efficiently. To do so, the warehouse manager needs to determine how many crates can be stacked in the storage room, as well as the total volume occupied by the crates.
The manager also needs to know the cube root of the total volume of a single crate in order to understand the spatial dimensions better.
Questions
1. How much volume does each crate occupy?
2. If the warehouse has a total volume of 1000 cubic meters, how many such crates can fit inside the warehouse, assuming that no space is left between the crates?
3. What is the cube root of the volume of one crate?
Sol 1
1. Volume of each crate: The side length of each crate is 8 meters. Therefore, the volume of one crate is.
𝑉 =
2. Number of crates=
Since only whole crates can be stored, the maximum number of crates that can fit is 1 crate.
3. The cube root of the volume of one crate is the side length of the crate. Since the volume is: 8 meters.
Q2
2. 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.
1. Calculate the area occupied by the fountain.
2. What will be the side length of the square lawn surrounding the fountain?
3. 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?
Sol 2
1. The area of a square is given by:
Area =
Here, the side length of the fountain is 2m : Area of the fountain =
2. Let the total area of the square lawn be A(lawn):
A(lawn) = 4 × A(fountain) = 4 × 4 = 16
3. The side length of a square can be found using the formula for its area: Side length =
Using A(lawn) = 16