NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2

The National Council of Educational Research, also known as NCERT, is self-governing. It was formed in 1961 by the Indian government. Its principal purpose is to assist the central and state governments in achieving the objective of raising the standard of education in the nation. The NCERT is tasked with conducting, organising, and promoting research in areas linked to academic study. They are responsible for producing all written material needed for educational purposes, including textbooks, bulletins, journals, educational kits, multimedia digital content, etc.

The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 for the Extramarks website are compiled by Mathematics professionals. The solutions are created by experts to help students comprehend the fundamentals. By using resources like the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2, students can advance with a firm foundation in the subject.

All elements of daily life are impacted by Mathematics because of its immense impact. In addition to serving as the foundation for human intellect and logic, Mathematics is essential to human endeavours to understand both the outside world and oneself. Since it promotes logical thinking and mental rigour, Mathematics is a useful instrument for developing mental discipline. Students may refer to the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 for guidance. Additionally, studying other academic topics like Physics, Social Studies, and to some extent, even Art requires a working knowledge of Mathematics.

Many students mistakenly believe that the Mathematics they are taught is worthless in everyday life. Students must understand the importance of Mathematics and debunk these misconceptions to study effectively for their exams. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 are one of the many tools available for students to take help from in their preparation, and they may use them by visiting the Extramarks website. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 are written by experts who are well-versed in the subject and have a complete understanding of the study material.

The most important thing for students to do is  practise as much as they can to grasp subjects like Mathematics. Students can use the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 for practise and revision. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 are excellent examples of solutions that are offered for various chapters in exercise-by-exercise order.

NCERT Solutions For Class 10 Maths Chapter 13 Surface Areas and Volumes (Ex 13.2) Exercise 13.2 

The Mathematics experts at Extramarks strive to provide resources for students that can benefit Class 10 students in a variety of ways. One of these resources is the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2. Students can quickly and easily access a variety of resources, including the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2, by just visiting the website. They do not need to look elsewhere on the internet for information to help them prepare for their board exams. The resources on the Extramarks website, including the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 are trustworthy sources of information.

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

The primary goal of CBSE is to improve skill development and teach students assessment and evaluation techniques that are job-related to help them direct themselves towards employment as well.The CBSE is in charge of establishing test specifications and holding board exams for classes 10 and 12. One of the most important tests a student will ever take is the Class 10 board exam. Depending on how well they perform in the Class 10 board exam, students get to select the stream in which they want to pursue future studies. As a result, Class 10 students are advised to take their board exams seriously.

The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 might help students prepare for their board exams. To prepare Class 10 students for their board exams, the school makes them appear for pre-board exams before the boards. The pre-board exam s goal is to acquaint students with the structure of the board exam and help them prepare better. To prepare for their pre-boards and boards, students can use tools like the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 and others.

 

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Class 10 Maths Ex 13.2 is one part of Chapter 13. The chapters are divided into different exercises in the NCERT books. Chapter 13 can have multiple exercises based on all the topics covered in the chapter. The NCERT books follow this pattern to make them easily understandable for everyone who uses them. For subjects like mathematics, the NCERT books follow a pattern of breaking down the content into different exercises to make the subject appear less intimidating and more manageable for students.The resources that are available on the Extramarks website are also prepared based on the same principles. The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 and other similar resources prepared by the experts for Class 10 Mathematics follow the same pattern of breaking down the content.NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes Exercise 13.2

The NCERT books are set up in a manner that makes it easier to understand how the subject matter is divided.. The specialists who developed the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 and other tools made sure that these tools are reliable and accurate. They do so while taking into consideration the CBSE official syllabus. The chapters become more difficult as the students continue to move up to the next standard. This is predicated on the fact that students get better as they approach the next standard.

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NCERT Solutions for Class 10 Maths Chapter 13 Exercises 

Geometric forms, Algebra, and other fields of Mathematics are just a few of the branches of Mathematics in Science that are concerned with numbers. The tools such as the NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 ,and numerous others available on the Extramarks website can help in understanding Mathematics better.

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Q.1 A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

Ans

Volume of the given solid=Volume of cone +Volume of hemisphere =13×πr2h+23πr3                                                    =13×π(1)2(1)+23π(1)3=π cm3

Q.2 Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Ans

Volume of air present in the model=Volume of cylinder                      +2×Volume of cone =πr2h+2×13×πr2h                                                    =π(32)2(8)+23π(32)2(2)                                                                           =66 cm2

Q.3 A gulab jamun, contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends with length 5 cm and diameter 2.8 cm (see the following figure)


Ans

Volume of one gulab jamun=Volume of cylinderical part       +2×Volume of hemispherical part =πr2h+2×23×πr3                                                    =π(1.4)2(2.2)+43π(1.4)3                                                             =25.05 cm3Volume of 45 gulab jamuns=45×25.05 cm3=1,127.25 cm3Volume of sugar syrup=30% of the volume of 45 gulab jamuns    =30100×1,127.25≈338 cm3

Q.4 A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see the following figure).


Ans

Volume of wood=Volume of cuboid −4×Volume cones =lbh−4×13πr2h                                   =15×10×3.5−43π0.52×1.4                                   =523.53 cm3

Q.5 A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

Ans

Let n lead shots were dropped in the vessel. Volume of water spilled=Volume of dropped lead shotsor 14×Volume cone=n×43πr23or 14×13πr12h=n×43πr23 or 52×8=n×16(0.5)3  or n=100 

Q.6 A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm3 of iron has approximately 8g mass. (Use π = 3.14)

Ans

Volume of the iron pole=Volume of a cylinder of height 220 cm and radius 12 cm +Volume of a cylinder of height 60 cm and radius 8 cm=π(12)2×220+π(8)2×60=1,11,532.8 cm3   Mass of 1 cm3 iron=8 gm∴Mass of 1,11,532.8 cm3 iron=8×1,11,532.8 gm=892.262 kg

Q.7 A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Ans

Volume of water left=Volume of a cylinder−Volume of a soloid=Volume of a cylinder−Volume of cone−Volume of hemisphere=πr2h1−13πr2h+23πr3=π602×180−13π602×120+23π603=π602×180−13π602×120−23π603=13π602540−120−120=13×227×3600×300=227×360000 cm3=227×0.36 m3=1.131 m3 (approx.)

Q.8 A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm3. Check whether she is correct, taking the above as the inside measurements, and π = 3.14.

Ans

Volume of vessel=Volume of sphere+Volume of cylinder=43πr13+πr22h=43π4.253+π12×8=346.51 cm3 (approx.)≠345Hence the child is not correct.  

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FAQs (Frequently Asked Questions)

1. What is Chapter 13 of Class 10 Mathematics about?

Chapter 13 of Class 10 Mathematics is divided into six sections from 13.1 to 13.6 and these all cover the sub-topics taught under the chapter. Chapter 13 teaches the topic ‘Surface Areas and Volumes’. The area or region that an object’s surface occupies is known as its Surface Area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in Geometry, including Spheres, Cubes, Cuboids, Cones, Cylinders, etc. Each form has its Volume and Surface Area. Chapter 13 talked about all these and more.

The NCERT Solutions for Class 10 Maths Chapter 13 Exercise 13.2 are the solutions to the questions based on the topic covered in Exercise 13.2 of Chapter 13. On the Extramarks website, the students can find the solutions for all six exercises in Chapter 13.

2. Can Extramarks’ NCERT Solutions be relied upon?

These solutions are compiled keeping in mind the most recent CBSE guidelines. Theyu are compiled by experts with years of experience. The professionals at Extramarks have developed a variety of useful materials that students may quickly access on the Extramarks website to aid in their understanding and mastery of Mathematics. Students can also access a wide variety of other study material and learning tools via the Extramarks’ website.