Apurva Institute
13. Surface Areas and Volumes-Assignments Mathematics Class 10 In English-CBSE Notes
Last Updated : 14 March 2026
Get updated Maths Concepts for mathematics for class 10 chapter 13. Surface Areas and Volumes Topic Assignments with clear explanations free access in English medium.
13. Surface Areas and Volumes-Assignments Mathematics Class 10 In English-CBSE Notes
Last Updated : 14 March 2026
13. Surface Areas and Volumes-Assignments Mathematics Class 10 In English-CBSE Notes
13. Surface Areas and Volumes
Assignments
Important Questions:
Q1. A hallow cone is cut by a plane parallel to the base and the uppar is removed. if the curved surface of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments into which the altitude of the cone is devided by the plane.
एक खोखले शंकु को उसके आधार के समांतर एक तल से काटा जाता है और उसका ऊपरी भाग हटा दिया जाता है | यदि शेष भाग का वक्र पृष्ठ का 8/9 भाग हो, तो तल के द्वारा काटे गए शंकु की ऊँचाई के दो भागों में अनुपात ज्ञात कीजिए |
Q2. A conical pot has radius 6 cm and height 8 cm which filled with water. A solid sphere is sunk so that it touches the cone. How much water flew out.
एक शंक्वाकार बर्तन जिसकी त्रिज्या 6 सेमी तथा ऊँचाई 8 सेमी है और पानी से भरा है एक ठोस गोला इस प्रकार डुबाया गया है कि डुबाने पर यह शंकु को स्पर्श करता है | ज्ञात कीजिए कि पानी का कितना हिस्सा बह कर निकल गया |
Q3. The height of the cone is 30 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume be 1/27 of the volume of the given cone at what height above the base is the section cut.
एक शंकु की ऊँचाई 30 cm है | एक छोटा शंकु इसके ऊपरी सिरे से आधार के समांतर एक तल से काटा जाता है | यदि इस काटे गए शंकु का आयतन दिए गए शंकु के आयतन का 1/27 वाँ भाग है बताइए की आधार से कितनी ऊँचाई से इसे काटा गया है |
Ans: 20 cm
Q4. A solid cylinder of radius ‘r’ cm and height ‘h’ cm is melted and changed into a right circular cone of radius ‘4r; cm. Find the height of the cone.
'r' cm त्रिज्या और 'h' c ऊँचाई वाले एक ठोस बेलन को पिघलाकर एक 4r त्रिज्या वाले लंब वृतीय शंकु ने बदला जाता है तो शंकु की ऊँचाई ज्ञात कीजिए |
Q5. A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio in their volumes?
एक बेलन, एक शंकु और e अर्द्धगोले का समान आधार और समान ऊँचाई है तो उनके आयतनों का अनुपात ज्ञात कीजिए |
Q6. A sphere of the radius ‘r’ is melted a form of the cone of height ‘r’. Find the radius of base of the cone.
एक r त्रिज्या वाले ठोस गोले को पिघलाकर इसे r ऊँचाई वाले एक शंकु के रूप में ढाला जाता है | इस प्रकार प्राप्त शंकु की आधार की त्रिज्या ज्ञात कीजिए |
Q7. A container shaped like a right circular cylinder having diameter 12 cm and height 21 cm is full of ice cream. The ice cream is to be filled into cone of height 12 cm and diameter 6cm, having a hemispherical shape on the top. Find the number of such which can be filled with ice cream.
ब्यास 12 cm और ऊँचाई 21 cm वाले एक वृतीय बेलन k आकार का बर्तन आइसक्रीम से पूरा भरा हुआ है | इस आइसक्रीम को 12 cm ऊँचाई और ब्यास 6 cm वाले शंकुओं से भरा जाना है, जिनका ऊपरी सिरा अर्द्धगोलाकार होगा | उन शंकुओं की संख्या ज्ञात कीजिए जो इस आइसक्रीम से भरे जाने हैं |
Q8. If a cone has the radius 6 cm and it is sectioned parallel to base, 8 cm from the top. Thus the obtained frustum’s radius is 2.4 cm (See the fig.) Find the height of the cone.
यदि एक शंकु की आधार की त्रिज्या 6 सेमी है और ऊपर से 8 सेमी की लंबाई लेकर आधार के समांतर काटा जाता है तो इस प्रकार प्राप्त छिन्नक का ऊपरी त्रिज्या 2.4 cm प्राप्त होता है | (देखिए आकृति) बताइए पूरी शंकु की ऊँचाई कितनी है ?
Q9. Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10km/hr. How much area will it irrigate in 30 minutes, if 8cm standing water is needed?
6 m चौड़ा और 1.5 m गहरी एक नहर 10 km/hr की गति से बह रही है | 30 मिनट में वह कितने क्षेत्र की सिंचाई करेगा, यदि 8 cm खड़े पानी की आवश्यकता हो |
Q10. Cost of applying gold water at the rate of Rs. 8 per cm2 on a hemispherical paper weight is Rs. 231. Find the radius of hemispherical paper weight.
एक अर्द्धगोलीय पेपर वेट के सम्पूर्ण पृष्ठ पर 8 रु प्रति सेमी की दर से सोने का पानी चढाने का खर्च 231 रु है | तो अर्द्धगोलीय पेपर वेट की त्रिज्या ज्ञात कीजिए |
Q11. A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs. 20 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs. 8 per 100 cm2 . (Take π = 3.14)
धातु की चादर से बना और ऊपर से खुला एक बर्तन के एक छिन्नक के आकार का है, जिसकी ऊँचाई 16 cm है तथा निचले ऊपरी सिरों की त्रिज्याएँ क्रमश: 8 cm और 20 cm हैं | 20 रु प्रति लीटर की दर से इस बर्तन को पूरा भर सकने वाले दूध का मूल्य ज्ञात कीजिए | साथ ही इस बर्तन को बनाने के लिए प्रयुक्त धातु की चादर का मूल्य 8 रु प्रति 100 cm2 की दर से ज्ञात कीजिए |
Why Our NCERT Solutions Is Matters For Your Study?
NCERT Solutions are one of the most trusted study resources for students preparing for school exams and board examinations. These solutions help students understand every concept clearly and improve their academic performance. In today’s competitive education system, simply reading the textbook is not enough. Students need proper explanations and accurate answers to understand topics in depth. That is why NCERT Solutions for Classes 6 to 12 are considered essential for effective learning and exam preparation.
On this page, students can find latest NCERT Solutions prepared according to the current CBSE syllabus. These solutions are created by subject experts to help students understand every question in a simple and easy way. With the help of chapter-wise NCERT answers, students can quickly revise important topics and strengthen their concepts. Whether you are preparing for school tests, annual exams, or board exams, these NCERT textbook solutions will guide you step by step.
NCERT Solutions for Class 10 mathematics Chapter 13. Surface Areas and Volumes Topic Assignments
NCERT Solutions for Class 10 mathematics Chapter 13. Surface Areas and Volumes Topic Assignments are prepared to help students understand important concepts of the chapter in a simple and clear manner. These solutions are based on the latest CBSE syllabus and follow the official NCERT textbooks. Students who are searching for accurate answers and step-by-step explanations can use these solutions to improve their learning and prepare better for school exams as well as board examinations.
In this section you will find Class 10 mathematics NCERT Solutions covering important questions, explanations and concept-based answers. Each question from the NCERT book is solved carefully so that students can understand how to write answers correctly in examinations. These solutions are also useful for quick revision before tests and assignments.
Why NCERT Solutions Are Important for Class 10 mathematics
NCERT books are considered the most reliable study material for CBSE students. Most examination questions are directly based on NCERT textbooks. Therefore studying NCERT Solutions for Class 10 mathematics helps students understand the exact pattern of questions and the correct method of answering them.
By practicing the questions from Chapter 13. Surface Areas and Volumes, students can strengthen their conceptual knowledge and improve their analytical thinking skills. These solutions also help students identify the most important topics and prepare effectively for school examinations.
About Chapter 13. Surface Areas and Volumes of Class 10 mathematics
Chapter 13. Surface Areas and Volumes is an important part of the Class 10 mathematics syllabus. This chapter explains several key concepts which are essential for understanding the subject in detail. Students often face difficulties while solving textbook questions related to this chapter. That is why NCERT Solutions for Chapter 13. Surface Areas and Volumes are provided to explain every concept in a simple and structured way.
The explanations provided here follow the official NCERT approach so that students can easily relate them to their textbook content. By studying these answers carefully, students can learn how to structure their answers and present them clearly in exams.
Understanding Topic: Assignments
The topic Assignments plays a significant role in Class 10 mathematics Chapter 13. Surface Areas and Volumes. Students must understand this topic clearly because it often appears in examinations in the form of short answer or long answer questions. The solutions provided here explain the topic in a step-by-step format so that students can easily grasp the concept.
By studying Assignments carefully, students can build a strong foundation in the subject and improve their overall academic performance. These solutions also help students revise the topic quickly before examinations.
Benefits of Using NCERT Solutions
- Concept clarity: Each answer explains the concept in simple language.
- Exam preparation: Solutions follow the CBSE exam pattern.
- Quick revision: Students can revise important questions quickly.
- Accurate answers: All solutions are based on the official NCERT textbook.
- Better understanding: Step-by-step explanations improve learning.
Students studying NCERT Solutions for Class 10 mathematics Chapter 13. Surface Areas and Volumes can easily understand the important points of the chapter. These solutions are also useful for completing homework assignments and preparing for tests.
Study NCERT Solutions in english
These solutions are available in english medium so that students can easily understand the concepts in their preferred language. Whether students are studying in Hindi medium or English medium, these solutions help them learn the subject more effectively and prepare confidently for examinations.
By practicing questions from Class 10 mathematics Chapter 13. Surface Areas and Volumes Topic Assignments, students can strengthen their conceptual understanding and improve their problem-solving skills.
Conclusion
In conclusion, NCERT Solutions for Class 10 mathematics Chapter 13. Surface Areas and Volumes Topic Assignments provide complete guidance for students who want to understand the chapter thoroughly. These solutions make learning easier, help students revise important concepts and improve their exam performance. Students should practice these answers regularly to build strong fundamentals and achieve better results in their examinations.
13. Surface Areas and Volumes-Assignments Mathematics Class 10 In English-CBSE Notes
Hindi Medium Students/Teachers/Tutors:
All Chapters mathematics Class 10
Class Wise NCERT Solutions
Students can find NCERT Solutions for Class 6, Class 7, Class 8, Class 9, Class 10, Class 11, and Class 12 on this page. Each class includes detailed solutions for important subjects such as Science, Mathematics, Social Science, English, and Hindi. These solutions are carefully prepared to ensure accuracy and clarity.
- NCERT Solutions for Classes 6 to 8 – Ideal for building strong basic concepts.
- NCERT Solutions for Classes 9 and 10 – Helpful for board exam preparation.
- NCERT Solutions for Classes 11 and 12 – Important for advanced concepts and competitive exams.
13. Surface Areas and Volumes-Assignments Mathematics Class 10 In English-CBSE Notes Study Materials For Class 6 to 12
Benefits of Studying with NCERT Solutions
Using online NCERT Solutions makes learning easier and more convenient. Students can access the study material anytime and anywhere using their mobile phone, tablet, or computer. This flexibility helps students manage their study time more efficiently and prepare better for exams.
- Easy online access anytime and anywhere.
- Time-saving preparation with ready solutions.
- Better practice with accurate answers.
- Effective revision before exams.
Improve Your Learning with NCERT Solutions
Regular practice with NCERT textbook solutions helps students strengthen their understanding of each subject. These solutions not only help students complete their homework but also improve their analytical and problem-solving skills. By studying chapter-wise answers, students can learn the correct way to write answers in exams and score better marks.
If you want to improve your academic performance, start studying with free NCERT Solutions for all classes. These solutions are designed to make learning simple, clear, and effective for every student. Choose your class, explore the chapters, and begin your preparation with the latest NCERT Solutions today.