by Tiwari Academy
NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes in English and Hindi Medium for CBSE Board Exams. NCERT Class 10 Math textbook chapter 12 Solution is revised as per CBSE Mathematics books released for Session 2024-25. Understanding NCERT Revised Solutions for Class 10 Mathematics Chapter 12 is quite easy. The NCERT Updated Solutions for Class 10 Maths Book Chapter 12 Surface Areas and Volumes provide a comprehensive guide to mastering this essential topic. With the formulas for surface areas and volumes, students can easily solve problems involving three-dimensional shapes such as cylinders, cones and spheres . The Class 10 NCERT Maths Textbook Chapter 12 Notes simplify complex concepts, ensuring a thorough understanding of the mathematical principles behind these shapes.
NCERT Solutions of Class 10 Maths Chapter 12 for CBSE Board
For a quick revision, NCERT Class 10th Math Chapter 12 Important Questions and Multiple Answers Question test your grasp of the topic and prepare you for exams. The solutions also include detailed explanations for the exercise problems, helping students develop a clear approach to problem-solving. Whether you’re working through Grade 10th Maths NCERT Book Chapter 12 Worksheets or tackling practice questions, these NCERT complete solutions serve as an invaluable resource for scoring well in your exams.
Class 10 Maths Exercise 12.1 in English
Class 10 Maths Exercise 12.2 in English
Class 10 Maths Exercise 12.1 in Hindi
Class 10 Maths Exercise 12.2 in Hindi
Benefits of NCERT Class 10 Maths Chapter 12 Study Material
The NCERT Textbook Class 10 Mathematics Chapter 12 Exercise Solutions PDF is a must-have for students preparing for their board exams. This downloadable material allows easy access to step-by-step explanations for each problem. The Class 10th Math Chapter 12 Question Bank includes a variety of problems, ranging from simple to advanced, ensuring a well-rounded practice experience. Students can also explore Surface Areas and Volumes NCERT 10th Examples to strengthen their understanding of real-world applications.
Class 10 Maths Chapter 12 Solutions for State Boards
Class 10 Maths Exercise 12.1
Class 10 Maths Exercise 12.2
Class 10 Maths Exercise 12.3
The revision notes and online test options make it easier to evaluate your preparation and identify areas for improvement. By using the study material and solving extra questions, students can enhance their problem-solving skills. The 10th NCERT Mathematics Chapter 12 Solutions ensure clarity and precision, making it easier to tackle complex problems during exams.
Important Points for Class 10 Maths Chapter 12: Surface Areas and Volumes
Key points include formulas for the surface areas and volumes of cylinders, cones, spheres and frustums. Understand unit conversions, real-world applications and solving problems step-by-step. Focus on NCERT exercise problems, important questions and examples to prepare thoroughly for board exams. Practice using revision notes and worksheets.
| Day | Topic | Tasks | Resources |
|---|---|---|---|
| Day 1 | Introduction to Surface Areas and Volumes | Understand basic concepts and formulas | NCERT textbook, Class Notes |
| Day 2 | Surface Area Calculations | Practice problems on surface areas of cylinders, cones, and spheres | NCERT exercise problems, Worksheets |
| Day 3 | Volume Calculations | Practice problems on volumes of various shapes | NCERT examples, Practice Questions |
| Day 4 | Frustums of Cones | Learn and apply formulas for frustums | Class 10 Maths Notes, NCERT Solutions |
| Day 5 | Mixed Problems | Solve mixed problems involving both surface areas and volumes | Important Questions, Extra Problems |
| Day 6 | Revision | Revise formulas and key concepts, solve mock tests | Revision Notes, Online Tests |
| Class: 10 | Mathematics |
| Chapter 12: | Surface areas and volumes |
| Content: | NCERT Textbook Exercises |
| Content Type: | PDF, Images, Text and Videos |
| Session: | CBSE 2024-25 |
| Medium: | English and Hindi Medium |
Class 10 Maths Chapter 12 all exercises (Ex. 12.1 and Ex. 12.2) for all boards. We have updated all the contents for new academic session 2024-25. UP Board students are now using NCERT Textbooks for their course and exams, so they can download UP Board Solutions for Class 10 Maths Chapter 12 exercises from the links are here. Contents are applicable for UP Board 2024-25 and CBSE Board in Hindi and English medium. Contents are free in PDF format to download without any login or registration. Download NCERT Solutions Online and Offline App for session 2024-25 based on updated NCERT Solutions and latest NCERT Books 2024-25. Previous year CBSE Exam question, important questions for practice are also given below. Download and practice to score good marks and solve your doubts easily.
10th Maths Chapter 12 Solutions
CBSE NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes exercises 12.1 and 12.2 are given here to download in PDF. All the solutions are updated for new academic session 2024-25 for UP Board, MP Board, Gujrat, CBSE board, etc., who are using latest NCERT Books for course.
Practical Applications of Surface Areas and Volumes
The Mathematics topic of Surface Areas and Volumes is not just an academic pursuit but a crucial skill for real-world problem-solving. The NCERT Class 10 Maths Book Chapter 12 Practice Questions and assignment tasks help students understand how these formulas are used in designing and constructing everyday objects. For instance, determining the amount of material required to manufacture a cylindrical tank or calculating the volume of a cone for storage purposes are practical applications covered in this chapter.
With the Class 10 Math NCERT Textbook Chapter 12 Solution Videos, students gain a visual understanding of these applications, making the learning process more interactive. Whether working on worksheets or revising using PDF downloads, students get a hands-on experience with mathematical concepts. This ensures they are not just exam-ready but also prepared for real-world challenges, making their preparation with NCERT Class 10 Mathematics Exercise Chapter 12 Solutions truly worthwhile.
Previous Years Questions
ONE MARK QUESTIONS
1. Volume and surface area of a solid hemisphere are numerically equal. What is the diameter of hemisphere? [CBSE 2017]
THREE MARKS QUESTIONS
1. A metallic solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm. How many cones will be made? [CBSE 2017]
FOUR MARKS QUESTIONS
1. In a hospital used water is collected in a cylindrical tank of diameter 2 m and height 5 m. After recycling, this water is used to irrigate a park of hospital whose length is 25 m and breadth is 20 m. If the tank is filled completely then what will be the height of standing water used for irrigation the park. Write your views on recycling of water. [CBSE 2017]
2. The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is 1/27 of the given cone, then at what height it is cut from its base? [CBSE 2017]
3. The height of a cone is 10 cm. The cone is divided into two parts using a plane parallel to its base at the middle of its height. Find the ratio of the volumes of the two parts. [CBSE 2017]
Objective of Surface areas and volumes
1. To identify situations where there is a need of finding surface area and where there is a need of finding volume of a solid figure and to find the surface areas & volumes of cuboids, cubes, cylinders, cones spheres and hemispheres, using their respective formulae. To solve some problems related to daily life situations involving surface areas and volumes of above solid figures.
2. In this chapter, we will deal with problems such as finding the area of sheet to covers a solid body, area of an object which is combination of two objects, finding the number of one object, required for creating another different object, finding the cost of ploughing a given field at a given rate, finding the cost of constructing a water tank with a particular capacity, finding area & volume of frustum (Frustum is a Latin word meaning ‘piece cut off’ and its plural form is ‘Frusta’) and the conversion of one solid into another solid on the basis of volume and so on.
For solving above type of problems, we need to find the perimeters and areas of simple closed plane figures (figure which lie in a plane) and surface areas and volumes of solid figures (figures which do not lie wholly in a plane). You are already familiar with the concepts of perimeters, areas, surface areas and volumes. In this chapter, we will study these in details.
Historical Facts! about Surface Areas and Volumes
Archimedes of Syracuse, Sicily, is remembered as the greatest Greek mathematician of the ancient era. He contributed significantly in geometry regarding the areas of plane figures and the areas and volumes of solid figures. He proved that the volume of a sphere is equal to two-third the volume of a circumscribed cylinder.
What topics are covered in NCERT Solutions for Class 10 Maths Chapter 12 Surface Areas and Volumes?
The NCERT Updated Solutions for Class 10 Mathematics Chapter 12 cover a variety of topics related to three-dimensional geometry. Students learn to calculate the surface areas and volumes of shapes like cylinders, cones, spheres and frustums. The solutions include exercise problems, important questions and examples that help in understanding the formulas and their real-world applications. With additional resources like revision notes, worksheets and extra questions, this chapter ensures a comprehensive grasp of the mathematical concepts. These resources are designed to simplify learning and improve problem-solving skills for board exams.
What are the topics to study in chapter 12 Surface Areas and Volumes of 10th Maths?
In chapter 12, Surface Areas and Volumes of class 10 math, students will study
- Surface Area of a Combination of Solids.
- Volume of a Combination of Solids.
- Conversion of Solid from one shape to another.
How can students benefit from Class 10 Maths Chapter 12 Notes and Study Material?
NCERT Class 10 Mathematics Chapter 12 Notes provide a concise and easy-to-understand summary of key concepts, making them ideal for quick revisions before exams. The study material, which includes practice questions, assignments and online tests, ensures students get ample exposure to a variety of problems. This boosts their confidence and ability to solve complex questions efficiently. The solutions PDF allows students to review step-by-step explanations anytime, helping them identify and correct mistakes. Together, these resources improve conceptual clarity and equip students with the skills needed to excel in exams and beyond.
Which topics students should revise before starting chapter 12 of class 10 Maths?
Before starting chapter 12 of class 10 Maths, Students should revise all the formulas mentioned in chapter 12 (surface areas and volumes) of class 9th Maths.
Where can students find additional practice for Surface Areas and Volumes?
Students can find extra practice for Surface Areas and Volumes Class 10 through various resources such as question banks, worksheets and important questions. The NCERT complete solutions also include a comprehensive set of Many Answers Question, examples and exercise solutions that cover different difficulty levels. For visual learners, solution videos provide detailed explanations, enhancing understanding and retention. These materials are often available as PDF downloads, making them accessible for both offline and online study. Solving these additional questions ensures students are well-prepared for exams and strengthens their problem-solving abilities.
Is there any optional exercise in chapter 12 of class 10th Maths?
Yes, there are no optional exercise in chapter 12 of class 10th Maths. Exercise 13.2 is challenging because this exercise contains logical questions which require higher-order thinking skills. Students find this exercise a little complex as compared to other exercises of this chapter.
How does Chapter 12 relate to real-world applications?
The concepts taught in Chapter 12 Surface Areas and Volumes have numerous real-world applications. For example, calculating the material required for constructing a cylindrical tank or the capacity of a cone-shaped container directly uses the formulas learned in this chapter. The Class 10 Mathematics Chapter 12 Examples and practice questions provide practical scenarios to demonstrate these applications. Students also learn to apply these calculations in fields like engineering, architecture and design. This not only prepares them for exams but also equips them with valuable skills for future studies and careers, making the chapter highly relevant.
Is chapter 12 of class 10th math difficult to solve?
Chapter 12 of class 10th Maths is not easy and not difficult. It lies in the middle of easy and difficult because some examples and questions of this chapter are easy, and some are difficult. However, the difficulty level of anything varies from student to student. So, Chapter 12 of class 10th Maths is easy or not depends on students also. Some students find it difficult, some find it easy, and some find it in the middle of easy and difficult.
