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CBSE Notes for Class 10 Mathematics chapter 13. Surface Areas and Volumes: Assignments, quick revision notes for Class 10 Mathematics chapter 13. Surface Areas and Volumes Assignments, Chapter-wise CBSE Revision Notes, CBSE Notes PDF Free Download, CBSE One Liner Notes Class 10, Half Yearly Revision Notes, CBSE Revision Notes Class 10 Mathematics
Get CBSE Notes for Class 10 Mathematics Chapter 13. Surface Areas and Volumes: Assignments prepared by experts as per the latest NCERT syllabus and CBSE exam pattern. These concise and easy-to-understand notes cover important definitions, formulas, diagrams, and key concepts from the chapter to help students in quick revision and effective exam preparation. Whether you are studying for school tests, board exams, or competitive exams, these notes provide a reliable study resource. Designed in simple language with point-wise explanations, they save time and enhance learning efficiency. Download free PDF notes, explore solved examples, and strengthen your understanding of [Topic Name] for scoring high marks. Perfect for Class 10 students who want clear, structured, and exam-oriented notes for CBSE Mathematics.
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 |
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