NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas And Volumes (Ex 13.5)

Mathematics is one of the most important and practical subjects that are taught to students in Class 10. The mathematical concepts taught in Class 10 can prove to be significant later in life too. There are a number of career opportunities available to Mathematics students, some of which are Engineer, Computer Programmer, Meteorologist, Market Researcher, Physicist, etc. It is important for students to have a good understanding of Mathematical concepts since they come in handy in everyday life as well. From keeping  track of finances to paying taxes, everything needs a basic understanding of Mathematics. Students who want to pursue a career in Engineering in particular need to work on improving their mathematical abilities as early as possible to get a head start. The majority of competitive examinations are based on the mathematical concepts taught in Class 10, so it is crucial that students pay attention to these concepts. The concepts taught in Class 10 Mathematics are mostly required to appear for competitive examinations since most of the competitive examinations are based on the basics of Class 10 Mathematics. Students should pay close attention to the mathematical topics covered in Class 10 if they intend on appearing for competitive examinations like the NEET, JEE Mains, JEE Advance, CAT, MAT, etc. Students of Class 10 may make use of the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 for the same.

The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 can be utilised by students as a resource to prepare for the CBSE Board Examination of Mathematics for Class 10. The Central Board of Secondary Education (CBSE) is a board that is popular and recognised nationwide. It is responsible for the administration of annual board examinations of Class 10 and Class 12. CBSE is also responsible for sanctioning the examination regulations and conditions for board examinations of Class 10 and Class 12. Students are urged to be aware of the fact that the CBSE board examinations are based on the NCERT curriculum. It is essential that students understand the significance of referring to the NCERT syllabus, as it focuses on the basics of each subject in accordance with the CBSE syllabus, which helps students secure higher marks in the CBSE board examinations. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 must be referred  for the preparation for the CBSE board examination. The NCERT curriculum has been designed with the CBSE board examinations in mind. Students are recommended to thoroughly practise the NCERT exercise problems and solutions. Students may acquire the NCERT solution from the Extramarks website. Students of Class 10 may also refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 for a better understanding of the concepts taught in Exercise 13.5 Class 10.

It is advised that students practise the NCERT exercise problems to attain a thorough understanding of the syllabus in relation to the CBSE board examination. Students get to choose their senior secondary subjects based on the marks they obtain in the CBSE Board Examination of Class 10. To obtain higher marks and be able to choose the field of their choice in the senior secondary classes, students must practice the NCERT exercise problems. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 can be accessed by students from the Extramarks website and mobile application. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 is also available in PDF format for students to download from the Extramarks website.

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas And Volumes (Ex 13.5) Exercise 13.5

Students are required to study keeping the NCERT syllabus of Mathematics in mind and to thoroughly obtain high marks in the CBSE Board Examination of Class 10 Mathematics. It is crucial that students practise the NCERT solutions consistently to score high marks in Mathematics. These topics need constant revision and practise for students to be able to have a good command of their mathematical skills. Students can practise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 available on the Extramarks website. It is essential that students have the knowledge of Ex 13.5 Class 10 Maths NCERT Solutions to have a good grasp of the concepts covered in Mathematics Chapter 13 named Surface Areas and Volumes. Students are encouraged to refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 from the Extramarks website.

Students must make a conscious effort to understand and comprehend the mathematical concepts covered in the Class 10 Mathematics syllabus. It is important for students to develop their comprehension skills in relation to mathematical concepts. This has a significant impact on the performance of students in Class 10 in the CBSE Board Examination of Mathematics. Students have the option to download the required learning material from the Extramarks website in PDF format. Extramarks has made this tool available to assist students in accessing the required study material effortlessly and efficiently. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 can also be downloaded by students from the Extramarks website or learning application. Students of Class 10 may access the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 from Extramarks for their preparation for the CBSE board examination. Students frequently find themselves unable to obtain learning resources for a variety of reasons, such as problems with their internet connection. In consideration of this, Extramarks has provided students with the option to download the required learning resources in PDF format from the Extramarks website. Students of Class 10 can download the  NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 in PDF format from the Extramarks website for their preparation for the CBSE Board Examination of Mathematics.

Extramarks provides study material with the requirements of all students in mind. Students of all classes from Class 1 to Class 12 can obtain study material for their preparation from the Extramarks website. The study material for competitive examinations can also be availed by students from the Extramarks website or mobile application. Extramarks provides online live sessions for students to be able to have an in-class experience from home. Extramarks also conducts doubt-solving sessions for students, these sessions are interactive for students to have an enhanced learning experience. In case students have any doubts, a doubt-solving session with regard to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 can be attended by students of Class 10. Extramarks provides study material for all classes of all boards. Students appearing for the CBSE board examination can refer to the study material provided by Extramarks since the Extramarks study material has been curated with the CBSE board examination perspective in mind. Students of Class 10 preparing for the CBSE Board Examination of Mathematics are urged to refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 which can be accessed from the Extramarks website.

Access NCERT Solutions for Class 10 Maths Chapter 13 – Surface Areas and Volumes

Students of Class 10 can access the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 from the EXtramarks website. Extramarks is a website well known for providing study material and learning resources to students for an enhanced learning experience. Extramarks provides complete syllabus coverage for all classes and boards. Students of all classes and boards can refer to Extramarks for their examination preparation. Students of Class 10 appearing for the CBSE Board Examination of Mathematics are suggested to study with the help of the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5.Students should practise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 on a regular basis for thorough preparation. It is crucial that students have a thorough understanding of the mathematical concepts taught in Class 10 Mathematics as they are foundational to clearing many competitive examinations like JEE IIT, NEET, AIIMS, CAT, MAT, etc. Practising consistently can help students gain clarity of the mathematical concepts that are crucial to clearing these competitive examinations. Mathematics Chapter 13 – Surface Areas and Volumes of Class 10 must be studied extensively by students. This can be done by repeatedly practising the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 provided by Extramarks. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 are useful for improving understanding of various mathematical concepts covered in Chapter 13 of the NCERT Mathematics book for Class 10.The NCERT Solutions for Class 10 Maths, Chapter 13, Exercise 13.5, can help you prepare for the CBSE Board Examination in Mathematics.

Mathematics is a subject that requires a lot of practice. It is important that students understand the significance of understanding the concepts covered in Class 10 Maths Ex 13.5. Students can acquire the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 from the Extramarks website. A lot of new mathematical formulae are introduced in Mathematics Chapter 13 of Class 10. Students must learn all the formulas that are taught in the concerned chapter. Learning formulas by heart can give students an advantage in the CBSE Class 10 Board Examination.Students must develop the skill of applying formulas to exercise problems and solving them in accordance with Class 10 Maths Exercise 13.5 Solution. Students are encouraged to refer to the study material provided on the Extramarks website for accurate and elaborated solutions. To have a better understanding of Class 10 Mathematics Chapter 13, students should repeatedly practise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 can be obtained by students from Extramarks.

NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes Exercise 13.5

The question paper format of the Central Board of Secondary Education is based on the NCERT syllabus, hence, it is advisable for students to refer to the NCERT exercise problems and solutions to prepare for the CBSE board examination. The CBSE board examination structure is primarily based on the NCERT curriculum. To prepare for the CBSE Board Examination of Class 10 Mathematics, students can obtain the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 from the Extramarks website. They must understand all the concepts covered in chapter 13 of the NCERT Mathematics book to perform well in the CBSE board examination.

Students should take into account the mark distribution of each topic covered in the concerned syllabus while preparing for the CBSE board examination. The topic weightage in the CBSE board examination must be taken into consideration during the preparation as it can help students in prioritising each topic in accordance with its importance. The topics covered in Mathematics Exercise 13.5 Class 10 hold significant importance in the CBSE board examination of Mathematics. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 can prove helpful in preparation for the CBSE board examination. Students must strive to understand the concepts covered in the concerned exercise to be well prepared for the final examination. To be able to prepare well for the CBSE board examination, they must strictly follow a timetable with a substantial amount of time allotted to each topic covered in the syllabus. Students can refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 for their preparation. Extramarks’ NCERT Solutions for Class 10 Maths, Chapter 13, Exercise 13.5 have been prepared by subject matter experts.The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 have been broken down into steps in an elaborate manner for students to better understand. Students are advised to begin preparing for the CBSE board examination at the start of the relevant academic year in order to perform better in the examination.For better results, they should practise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5.

Students can access learning resources for the CBSE board examination from the Extramarks website. Extramarks provides study material that has been designed by experts in accordance with the NCERT syllabus and guidelines. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 are concerned with deriving the surface area or volume of a particular object with the help of different formulas that have been introduced in the chapter. It is essential for students to understand the basis that determines the appropriate formula application to effectively solve the problems of Mathematics Chapter 13, Exercise 13.5 of Class 10. To score high marks in the CBSE Board Examination of Class 10, students must regularly practise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 provided on the Extramarks website. They can also use the revision notes in the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5. Extramarks also provides in-depth performance reports to help students track their progress in terms of their preparation. Students have the provision of attending online live sessions with respect to their preparation of the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 for an in-depth and thorough understanding of the concerned topic. Students are suggested to practise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 regularly to score higher marks in the CBSE board examination.

Q.1 A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.

Ans

One round of wire covers 3 mm height of cylinder.Number of rounds=Height of cylinderDiameter of wire=12 cm3 mm=12 cm0.3 cm=40Length of wire required in one round=Circumference of cylinder                                                                              =2πr=2π×102=10π cmLength of wire in 40 rounds=40×10π=40×10×3.14=1256 ​ cmRadius of wire=0.32 cm=0.15 cmVolume of wire= Area of cross section of wire×Length of wire                                 =3.14×0.152×1256  cm3=88.7364 cm3Mass=Volume×Density=88.7364×8.88=787.979232 gm = 788 gm (approx.)

Q.2 A right triangle, whose sides are 3 cm and 4 cm (other than hypotenuse) is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Choose value of π as found appropriate.)

Ans

The double cone formed by revolving right-angled ΔABCabout hypotenus AC is shown above.AC=32+42=5 cm         Area of ΔABC=12×AB×BC=12×3×4=6 cm2or, 12×AC×OB=6or, 12×5×OB=6or, OB=125=2.4 cmVolume of double cone      =Volume of cone 1+Volume of cone 2      =13πr2h1+13πr2h2      =13π(2.4)2(h1+h2)  =13π(2.4)2×5=30.14 cm3Surface area of double cone=Surface area of cone 1                                +Surface area of cone 2                            =πrl1+πrl2 =3.14×2.4(3+4)=52.75 cm2

Q.3 A cistern, internally measuring 150 cm × 120 cm × 110 cm, has 129600 cm3 of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each brick being 22.5 cm × 7.5 cm × 6.5 cm?

Ans

Volume of cistern=150×120×110=1980000 cm3Volume to be filled in cistern=1980000−129600=1850400 cm3Let n number of porous bricks were placed in cistern.So, volume of n bricks=n×22.5×7.5×6.5=1096.875nEach brick absorbs one-seventeenth of its volume.∴Volume absorbed by n bricks=n17(1096.875)Now,   Volume to be filled in cistern+Volume absorbed by n bricks        =Volume of n bricksor, 1850400+n17(1096.875)=1096.875nor, n=1792.41So, 1792 bricks can be put in the given cistern.

Q.4 In one fortnight of a given month, there was a rainfall of 10 cm in a river valley. If the area of the valley is 7280 km2, show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each 1072 km long, 75 m wide and 3 m deep.

Ans

Rainfall = 10 cm = 0.1 mArea of the valley = 7280 km2Vaolume of rainfall in the valley = 7280 × 1000 × 1000 × 0.1m3                                       = 728000000 m3Volume of water in 3 revers = 3 × 1072000 × 75 × 3 = 723600000 m3Thus, the total rainfall is approximately same as the totalvolume of the three rivers.

Q.5 An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and the diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel (see the following figure).

Ans

Height of frustum=h1=22−10=12 cmHeight of cylindrical part=h2=10 cmR of lower end=r1=82 =4 cmR of end=r2=182 =9 cmS =l=r1−r22+h12                                                   =4−92+122 = 13 Areaoftinsheetrequired =CSA of frustum part+CSA of cylindrical part =πr1+r2l+2πr1h2=2274+9×13+2×227×4×10=78247 cm2

Q.6 Derive the formula for the curved surface area and total surface area of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.

Ans

Let ABC be a cone. A frustum DECB is cut by a plane parallelto its base.In ΔADF and ΔABG,          DFBG=AFAG=ADABor r2r1=h1−hh1=l1−ll1or r2r1=1−hh1=1−ll1or 1−ll1=r2r1or ll1=1−r2r1=r1−r2r1or l1l=r1r1−r2

CSA of frustum DECB=CSA of cone ABC−CSA of cone ADE                                              =πr1l1−πr2(l1−l)   =πr1(lr1r1−r2)−πr2(lr1r1−r2−l) =πr12lr1−r2−πr2(lr2r1−r2)                                              =πr12lr1−r2−πr22lr1−r2=π(r1+r2)lCSA of frustum=π(r1+r2)lTotal surface area of frustum=CSA of frustum+                                               +CSA of upper circular end                                               +CSA of lower circular end                        =π(r1+r2)l+πr12+πr22                        =π[(r1+r2)l+r12+r22]

Q.7 Derive the formula for the volume of the frustum of a cone, given to you in Section 13.5, using the symbols as explained.

Ans

Let ABC be a cone. A frustum DECB is cut by a plane parallelto its base.In ΔADF and ΔABG,          DFBG=AFAG=ADABor r2r1=h1−hh1=l1−ll1or r2r1=1−hh1=1−ll1or  hh1=r1−r2r1

Volume of frustum DECB=Volume of cone ABC− Volume of cone ADE                                                     =13πr12h1−13πr22(h1−h)           =π3[r21h1−r22(h1−h)]            =π3[r21r1hr1−r2−r22(r1hr1−r2−h)]                                                   =π3[r21r1hr1−r2−r22(r2hr1−r2)]                                                  =πh3[r13−r23r1−r2]=πh3(r21+r22+r1r2)

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FAQs (Frequently Asked Questions)

1. How can students prepare for the Class 10 CBSE Board Examination of Mathematics?

Students can acquire the required study material for the preparation of the CBSE board examination of Mathematics from the Extramarks website or mobile application. Extramarks is one of the most reliable and trusted educational websites known for providing adequate learning resources to students. They can find up-to-date information concerning the CBSE Board examination on the Extramarks website. Students of Class 10 can refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 provided on the Extramarks website for their preparation. Students can also access other study material for their preparation from the Extramarks website, like revision notes, previous years’ papers, mock tests, sample papers, online live sessions, and many more. They are recommended to solve sample papers of the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 to strengthen their mathematical skills. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 have been designed by experts in an elaborate manner. Students are encouraged to utilise the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 available on the Extramarks website, for a step-by-step breakdown of the solutions.

2. Why is it recommended to refer to Extramarks for the preparation of the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5?

Extramarks is one of the most renowned and reliable educational websites that provides students with learning resources to prepare for examinations. Extramarks provides learning resources for all classes of all boards. Class 10 Students appearing for the CBSE board examination of Mathematics are advised to refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 provided on the website of Extramarks. Students can also download the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5 in PDF format. To have a better understanding of the concepts and formulas covered in Chapter 13 of Class 10 Mathematics, it is recommended to make use of the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.5.