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NCERT Solutions for Exercise 13.2 Class 10 Maths Chapter 13 - Surface Area and Volumes

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NCERT Solutions for Exercise 13.2 Class 10 Maths Chapter 13 - Surface Area and Volumes

Edited By Ramraj Saini | Updated on Nov 27, 2023 05:35 PM IST | #CBSE Class 10th

NCERT Solutions For Class 10 Maths Chapter 13 Exercise 13.2

NCERT Solutions for Exercise 13.2 Class 10 Maths Chapter 13 Surface Area and Volumes are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. Class 10 Maths ex 13.2 is concerned with calculating volumes when two or more objects are combined to form a new shape. Unlike the surface area calculation in the previous section, where some of the areas that were not visible were left out, this would not be the case with volume. The volume of the solid created by merging two basic solids of known figure equals the total volume of the constituent solids.

This exercise has eight questions that require students to visualize the shapes as described in the problem statements, then break up the figure, especially those types of figures whose volume or the formula to find its volume is known to us. So that we can very easily determine their volumes and either add them or subtract them to get the final volume of the final resultant figure. 10th class Maths exercise 13.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below

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Surface Areas and Volumes Class 10 Maths Chapter 13 Exercise: 13.1

Q1 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 \pi .

Answer:

The volume of the solid is given by :

The volume of solid = Volume of cone + Volume of a hemisphere

The volume of cone :

=\ \frac{1}{3} \pi r^2h

or =\ \frac{1}{3} \pi \times 1^2\times 1

or =\ \frac{\pi}{3}\ cm^3

And the volume of the hemisphere :

=\ \frac{2}{3}\pi r^3

or =\ \frac{2}{3}\pi \times 1^3

or =\ \frac{2\pi}{3}\ cm^3

Hence the volume of solid is :

=\ \frac{\pi}{3}\ +\ \frac{2\pi}{3}\ =\ \pi\ cm^3

Q3 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 Fig).

1636092497555

Answer:

It is clear from the figure that gulab jamun has one cylindrical part and two hemispherical parts.

Thus, the volume of gulab jamun is = Volume of cylindrical part + 2 (Volume of the hemisphere )

Now, the volume of the cylinder is =\ \pi r^2h

or =\ \pi\times 1.4^2\times 2.2

or =\ 13.55\ cm^3

And the volume of a hemisphere is :

\\=\ \frac{2}{3}\pi r^3\\\\=\ \frac{2}{3}\times \pi \times (1.4)^3\\\\=\ 5.75\ cm^3

Thus the volume of 1 gulab jamun is = 13.55 + 2 (5.75) = 25.05 cm^3.

Hence the volume of 45 gulab jamun =\ 45(25.05)\ cm^3\ =\ 1127.25\ cm^3

Further, it is given that one gulab jamun contains sugar syrup upto 30 \% .

So, the total volume of sugar present :

=\ \frac{30}{100}\times 1127.25\ =\ 338\ cm^3

Q5 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.

Answer:

According to the question :

Water spilled from the container = Volume of lead balls.

Let us assume the number of lead balls to be n.

Thus the equation becomes :

\frac{1}{4}\times Volume_{cone}\ =\ n\times \frac{4}{3} \pi r^3

or \frac{1}{4}\times \frac{1}{3}\pi\times5^2\times 8\ =\ n\times \frac{4}{3} \pi\times 0.5^3

or n\ =\ \frac{25\times 8}{16\times \left ( \frac{1}{2} \right )^3}

or n\ =\ 100

Hence the number of lead shots dropped is 100.

Q6 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 cm 3 of iron has approximately 8g mass. (Use \pi = 3.14 )

Answer:

The pole can be divided into one large cylinder and one small cylinder.

Thus, the volume of pole = volume of large cylinder + volume of a small cylinder

=\ \pi r_l^2h_l\ +\ \pi r_s^2h_s

or =\ \pi \times 12^2\times 220\ +\ \pi \times 8^2\times 60

or =\ \pi \times \left ( 144\times 220\ +\ 64\times 60 \right )

or =\ 3.14\times 35520

or =\ 111532.5\ cm^3

Now, according to question mass of the pole is :

=\ 8\times 111532.5

or =\ 892262.4\ g\ =\ 892.262\ Kg

Q7 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.

Answer:

It is clear from the question that the required volume is :

The volume of water (left) =Volume of a cylinder - Volume of solid

Now the volume of the cylinder is =\ \pi r^2h

or =\ \pi\times (60)^2\times 180\ cm^3

And the volume of solid is :

\\=\ \frac{1}{3} \pi r^2h\ +\ \frac{2}{3}\pi r^3\\\\=\ \frac{1}{3} \times \pi \times (60)^2\times 120\ +\ \frac{2}{3}\times \pi \times (60)^3\\\\=\ \pi (60)^2\times 80\ cm^3

Thus the volume of water left :

\\=\ \pi (60)^2\times 180\ -\ \pi (60)^2\times 80\\\\=\ \pi (60)^2\times 100\\\\=\ 1131428.57\ cm^3\\\\=\ 1.131\ m^3

Q8 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 cm 3 . Check whether she is correct, taking the above as the inside measurements, and \pi = 3.14 .

Answer:

The volume of the vessel is given by :

The volume of vessel = Volume of sphere + Volume of the cylindrical part

Now, the volume of the sphere is :

\\=\ \frac{4}{3}\pi r^3\\\\=\ \frac{4}{3}\pi \left ( \frac{8.5}{2} \right )^3\\\\=\ 321.55\ cm^3

And the volume of the cylinder is:-

\\=\ \pi r^2h\\\\=\ \pi \times (1)^2\times 8\\\\=\ 25.13\ cm^3

Thus the volume of the vessel is = 321.55 + 25.13 = 346.68\: cm^3



More About NCERT Solutions for Class 10 Maths Exercise 13.2

NCERT Solutions for Class 10 Maths exercise 13.2- The most important part of NCERT solutions for Class 10 Maths chapter 13 exercise 13.2 is that it helps you to determine how to break the figure in those parts or shapes with which we are familiar and we know their formulas. For example – In the question given in number 2 of exercise 13.2, we have broken the shape using two cones and one cylinder because we are familiar with these shapes. We should also know different formulas like formulas for finding the volume of cones, cylinders etc.

Some important formulas are:

Volume of cube = 1639997017268

Volume of cylinder 1639997016279

Also Read| Surface Areas and Volumes Class 10 Notes

Benefits of NCERT Solutions for Class 10 Maths Exercise 13.2

  • Exercise 13.2 Class 10 Maths, is based on Volume of a Combination of Solids.
  • Class 10 Maths chapter 13 exercise 13.2 helps us in understanding complex shapes and finding its volume.
  • Class 10 Maths chapter 13 exercise 13.2 helps us to simplify complex shapes by breaking it into smaller individual objects that are simple to our understanding.

Key Features For Class 10 Maths Chapter 13 Exercise 13.2

  • Step-by-Step Solutions: Clear and detailed explanations for each problem in Ex 13.2 class 10, ensuring students understand the methodology.
  • Conceptual Understanding: Explanation of surface area and volume concepts involved in the exercises, aiding students in grasping the underlying principles are discussed in class 10 maths ex 13.2.
  • Variety of Problems: In class 10 ex 13.2, diverse types of problems, offering a broad spectrum of challenges to reinforce understanding.
  • Visual Aids, Diagrams, and Examples: Use of visual representations, diagrams, and real-life examples to simplify complex concepts and aid visual learners.
  • Application-Based Problems: In 10th class maths exercise 13.2 answers, application-oriented problems that relate statistics to real-world scenarios, fostering practical understanding and problem-solving skills.

Also See:

NCERT Solutions Subject Wise

Frequently Asked Question (FAQs)

1. What is the core concept of NCERT solutions for Class 10 Maths exercise 13.2?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

2. Write the formula for finding the volume of cone, cylinder and sphere?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

3. If a cone and a hemisphere of same radius are placed on one another such that the hemisphere lies in the bottom of the arrangement, find the total volume of the arrangement?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

4. If a cylinder and a hemisphere of same radius are placed on one another such that the cylinder lies in the bottom of the arrangement, find the total volume of the arrangement?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

5. How many cubes of side ‘x’ is required to make a new cube of side ‘2x’?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

6. A cube of ‘x’ is placed below a sphere such that the diameter of the sphere is equal to the diagonal of the face of the cube. Find the total volume of the arrangement?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

7. A hemisphere is removed from the bottom of a cylinder of radius ‘r’ and height ‘3r’ find the volume of the remaining portion?

The core concept behind this exercise is to find the volume combination of solids. We have to remember the formula for finding the volume of cuboid, sphere, cylinder etc

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A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

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Option 1)

2,000 \; J - 5,000\; J

Option 2)

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Option 3)

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Option 4)

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K/2\,

Option 2)

\; K\;

Option 3)

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Option 4)

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Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

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Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

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Option 1)

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Option 2)

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Option 3)

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Option 1)

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Option 3)

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Option 4)

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Option 1)

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Option 2)

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Option 3)

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Option 1)

twice that in 60 g carbon

Option 2)

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Option 1)

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Option 2)

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Option 3)

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The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
Videographer
2 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

5 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Linguist

Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning). 

Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian

2 Jobs Available
Public Relation Executive
2 Jobs Available
Travel Journalist

The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
4 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Production Manager
3 Jobs Available
Merchandiser
2 Jobs Available
QA Lead

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans. 

2 Jobs Available
Metallurgical Engineer

A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment. 

2 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
QA Manager
4 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
ITSM Manager
3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
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