Extra Curriculum Support
Enhanced 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. Define a polyhedron. Give an example.
2. What is a net? Explain its use in forming 3D shapes.
3. Name the faces, edges, and vertices of a cube.
4. Differentiate between a prism and a pyramid.
5. Draw the net of a triangular prism.
6. What is the difference between a 2D shape and a 3D shape?
7. Name two objects from your surroundings that resemble a cone and a cylinder.
8. Identify the shapes of the faces of a cuboid.
Sec B
1. Draw the net of a cube and explain how it folds into a cube.
2. List the properties of a sphere and a cylinder.
3. How many faces, edges, and vertices does a triangular pyramid have? Verify using Euler’s formula.
4. Compare and contrast a cube and a cuboid in terms of faces, edges, and vertices.
5. Identify and draw the front view, top view, and side view of a cone.
6. If a solid has 6 faces, 12 edges, and 8 vertices, identify the solid and explain.
7. Draw a net for a rectangular prism and label its dimensions.
Sec C
1. Draw the net of a cylinder and explain how it forms the 3D shape.
2. Explain with diagrams how a sphere differs from a hemisphere.
3. Discuss the relationship between 2D and 3D shapes with examples.
4. Draw a net for a cube, label its faces, and show how numbers can be arranged to make it a die.
5. Describe the properties of a cone and a cylinder. Compare them with a sphere.
6. Identify the 3D shape from its 2D views: front view, top view, and side view.
Sec D
1. Draw and explain the nets for the following solids: cube, cuboid, and triangular prism.
2. Identify and draw the 2D views (top, front, side) of a square pyramid, a cylinder, and a sphere.
3. Explain the role of symmetry in visualizing solid shapes with examples.
4. Discuss how to construct the net of a hexagonal prism. Show the steps with a diagram.
5. Solve: A solid has 10 faces, 16 vertices, and 24 edges. Verify if it satisfies Euler’s formula.
6. Draw and explain the cross-sections of a cylinder, cone, and sphere.
Problem 1
How can understanding and using solid shapes inspire sustainable design practices, such as reducing material waste in packaging or construction?
Problem 2
In a group activity to create models of solid shapes, how can teamwork and mutual respect contribute to achieving better results and fostering collaboration?
Q1
A cube and a cuboid have the same volume. If the edge of the cube is 5 cm, what could be the possible dimensions of the cuboid? Discuss how the shapes differ in terms of surface area and practical applications.
Q2
Imagine you are tasked with designing a water tank in the shape of a cylinder. How would you calculate the capacity and ensure that the shape is both space-efficient and structurally stable? Explain your reasoning.
Questions
1.Name two 3D shapes that have curved surfaces.
2. Which 3D shape is formed by rotating a rectangle about one of its sides?
3. Identify which of the following nets can form a cube.
4. Draw the net of a triangular prism.
5. What will the top view of a cone look like?
6. Sketch the front view, top view, and side view of a cuboid.
7. If you cut a cylinder horizontally, what shape is the cross-section?
8. What is the cross-section of a cube when cut diagonally?
9. Draw an isometric sketch of a cube.
10. Create an isometric sketch for a cuboid with dimensions 3×2×1.
11. What shape is the shadow of a sphere when illuminated from above?
12. If a cuboid is illuminated from the front, what shape will its shadow be?
13. How many lines of symmetry does a square pyramid have?
14. Does a cone have rotational symmetry? If yes, what is the order?
15. Can a cube have a curved surface? Why or why not?
16. Explain why a sphere has no edges or vertices.
Q1
Case Study:
A toy manufacturing company is designing a new toy using geometric shapes. The toy consists of:
A cylinder as the base with a height of 10 cm and a radius of 4 cm.
A cone placed on top of the cylinder with the same base radius and a height of 6 cm.
A hemisphere placed on top of the cone with the same radius.
The company wants to calculate:
1. The total height of the toy.
2. The total surface area (excluding the base of the cylinder).
3. The volume of the toy.
Sol
Solution :
1. Total Height
The height of the toy is the sum of the heights of the cylinder, cone, and hemisphere.
Total Height = Height of Cylinder + Height of Cone+Radius of Hemisphere
Total Height = 10 + 6 + 4 = 20cm
2. Total Surface Area (Excluding the Base)
1. Curved surface area (CSA) of the cylinder:
CSA of Cylinder = 2πrh = 80π
2. CSA of the cone =
CSA of Come = πrl = 28.84π
3. CSA of the hemisphere = 2π
Total Suraface Area = 80π = 140.84π
Total Suraface Area = 442.6
3. Total Volume
1. Volume of the Cylinder: π
2. Volume of the Cone:
3. Volume of the Hemisphere:
Total Volume = 160π + 32π + 42.67π = 234.67π
Total Volume = 737.2