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Learn Combination of solids

Combining Solids to Find New Volumes video thumbnail

Combining Solids to Find New Volumes

Welcome to the fascinating world of 3D geometry in your CBSE Class 9 Mathematics syllabus! In the chapter "Surface Area and Volumes," you have already mastered calculating the properties of basic, individual shapes like cubes, cylinders, cones, and spheres. However, the real world rarely consists of single, isolated shapes. Think of an ice cream cone, a circus tent, or a medicine capsule. These are all perfect examples of a Combination of Solids. This mathematical concept involves joining two or more basic 3D geometric figures together to form a new, complex shape. Understanding how to find the total surface area and volume of these composite figures is crucial for solving real-life structural and design problems.

To master the mathematics behind composite solids, you must clearly distinguish between calculating their volume and their surface area. The fundamental logic for Volume is straightforward: the total space occupied by the composite solid is exactly equal to the sum of the volumes of its individual components. For instance, Total Volume = Volume of Solid 1 + Volume of Solid 2. However, finding the Total Surface Area (TSA) of a combined solid requires careful visualization. When two solids are joined together, their overlapping faces are hidden and are no longer exposed to the outside. Therefore, you should never blindly add the individual total surface areas of the separate shapes. Instead, the core logic is to add only the Curved Surface Areas (CSA) of the visible parts, plus any remaining exposed bases. For example, if you join a cylinder and a hemisphere, the flat circular base where they connect is trapped inside and ignored in your TSA calculation.

Analyzing a Combined Solid: The Medicine Capsule Hemisphere 1 CSA = 2πr² Central Cylinder CSA = 2πrh Hemisphere 2 CSA = 2πr² r h (height of cylinder) r Total Surface Area = 2πr² + 2πrh + 2πr² = 2πr(2r + h)

Take a close look at the diagram above, which illustrates a classic exam problem: a medicine capsule. The visual perfectly demonstrates how a complex composite solid is constructed by fusing a central cylinder with two identical hemispheres at its ends. Notice the boundaries and structural dimensions; they emphasize that the circular bases of the cylinder and the flat bases of the hemispheres are completely hidden inside the shape where they attach. Because these internal faces are not exposed to the outside, they are entirely excluded from the total surface area. As shown in the green formula box, the Total Surface Area (TSA) of the capsule is found by adding the Curved Surface Area (CSA) of the first hemisphere, the CSA of the cylinder, and the CSA of the second hemisphere, yielding the simplified formula 2πr(2r + h). In your CBSE Class 9 exams, you will frequently use this exact step-by-step approach to solve practical problems, such as calculating the cost of painting a wooden toy, wrapping a pillar, or finding the air capacity of an industrial shed.

Mastering 3D geometry and visualizing the combination of solids can sometimes be tricky, but you do not have to tackle it alone! If you want to strengthen your fundamentals, practice complex calculations, or need step-by-step guidance to excel in your CBSE exams, UrbanPro is here to help. As India's most trusted learning network, UrbanPro connects you with highly experienced, verified Class 9 Mathematics tutors who specialize in making complex mathematical concepts easy to understand. Whether you prefer one-on-one online tuition from the comfort of your home or interactive local offline classes, explore UrbanPro today to find the perfect tutor and boost your confidence in Mathematics!


Other Concepts in Surface Area and Volumes


Other Concept Videos for Combination of solids

Combining Solids to Find New Volumes video thumbnail

Combining Solids to Find New Volumes

CBSE - Class 9>Mathematics>Surface Area and Volumes>Combination of solids


Combining Solids to Find New Volumes video thumbnail

Combining Solids to Find New Volumes

CBSE - Class 9>Mathematics>Surface Area and Volumes>Combination of solids

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superTutorSuper Tutor
locationImg Sector 92, Gurgaon
20 yrs of Exp 20 students
greenClock 1275 hrs of classes completed
rsIcon 800 per hour
Teaching mathematics since last 20 years. Doing research on Vedic mathematics
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Teaching since last 20 years

Nandini Mishra

Amit ji is a fantastic teacher. My daughter is very happy with her studies. He is exactly what she needed, a teacher with deep understanding of his subject and a very good communicator. If there is one gripe that I may mention, it's time. We would love to have more classes to cover Physics, but he is completely booked for his time. I would highly recommend him. Thank you.

Skills: Mathematics , Physics and more
Also teaches: Vedic Maths Training, BSc Tuition and more

Sai V. Class 9 Tuition trainer in Madappanahalli
(138)
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locationImg Itagalpura Main Rd, Madappanahalli
17 yrs of Exp 43 students
greenClock 3515 hrs of classes completed
rsIcon 400 per hour
MSc, BEd , (Phd), Member of Royal Society UK
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I gained extensive experience in delivering high-quality education following the CBSE/ICSE curriculum. My key responsibilities included: Classroom Teaching: Effectively taught Mathematics, Physics and Chemistry to students of classes IX, ensuring alignment with the CBSE/ ICSE syllabus and fostering a deep understanding of key concepts. Curriculum Planning: Designed and implemented lesson plans that adhered to the CBSE guidelines, ensuring comprehensive coverage of topics while keeping in mind the varying learning needs of students. Student Assessment: Created and administered tests, quizzes, and assignments in accordance with the CBSE exam pattern. Monitored student performance and provided constructive feedback to facilitate continuous improvement. Interactive Learning: Encouraged an interactive classroom environment, integrating various teaching aids such as multimedia presentations, hands-on activities, and group discussions to enhance student engagement and understanding. Preparation for Board Exams: Provided focused support for students appearing for their CBSE/ICSE board exams by conducting regular revision sessions, mock tests, and personalized guidance to help them excel. Parental Communication: Maintained regular communication with parents regarding student progress, attendance, and overall development. Organized parent-teacher meetings to ensure a collaborative approach to student growth. Co-curricular Involvement: Actively participated in school events, projects, and extracurricular activities, fostering holistic development among students. Professional Development: Engaged in continuous professional development through workshops and CBSE training programs to stay updated with the latest educational practices and policies.

Skills: Mathematics , Physics and more
Also teaches: NEET-UG Coaching, Class 10 Tuition and more

(59)
superTutorSuper Tutor
locationImg Sector 5, Dwarka, Delhi
10 yrs of Exp 32 students
greenClock 1149 hrs of classes completed
rsIcon 500 per hour
10 Yrs in Teaching, Conduct Batch Of Two Kids, One-to-One classes. ShortTermPrep & LongTermClasses.
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I teach Math and Science to 8th-12th standard students and have been teaching for more than 10 years. Batch of 2 Students: I conduct these small batches with a pair of students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). Works for those students/parents who are looking for individual attention for their kids but still want it to be a little affordable. *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 4500/- per month/12 classes. Batch of 6 Students: I conduct these small batches with 5-6 students of the same class and the education board (I cover all popular boards CBSE, ICSE, IGCSE etc.). *4 classes per week (So 16 a month) *Maths and Science *Fee Rs. 4000/- per month/16 classes. I will start the classes immediately once the first kid enrolls. ------------------------------------------------------------------------------- Individual/Private/One-to-One classes: I conduct these one to one classes for those students willing to have one to one setup (I cover all popular boards CBSE, ICSE, IGCSE etc.). *3 classes per week (So 12 a month) *Maths and Science (Also English Grammar and Literature) *Fee Rs. 7000/- per month/12 classes. ------------------------------------------------------------------------------- I took classes and batches in different institutions.

Surabhi rai

The teacher is very good. He understands the students strength and weakness and decides the pace of learning. He also tries to make the student comfortable and at ease with his/her capacity and then works on the child. It is not just Math he works on but the child's confidence and comfort with the subject. Highly recommended.

Skills: Mathematics , Physics and more
Also teaches: Class 10 Tuition, Class 8 Tuition and more

Avishake Chatterjee Class 9 Tuition trainer in Kolkata
(62)
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locationImg Behala, Kolkata
8 yrs of Exp 7 students
greenClock 947 hrs of classes completed
rsIcon 700 per hour
MATHS EXPERT having an experience of 6+years
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As a passionate mathematics teacher, I have always enjoyed imparting knowledge to others. I am a B.Tech graduate in Electronics and Communication. I have been teaching mathematics for over four years, and my love for the subject has grown stronger with time. I started teaching as a part-time tutor while pursuing my engineering degree and fell in love with the profession. After completing my degree, I worked with Byjus, one of the leading Edtech companies in India, as a mathematics teacher for two years. While I enjoyed my time at Byju's, I could do more as a teacher and wanted to explore new avenues. I joined Vedantu, an online learning platform, where I have been teaching mathematics for the last two years. I started my journey as a math teacher out of pure passion. Mathematics has always been my favourite subject, and I enjoyed solving problems and equations from a young age. As I grew older, I realised I had a natural talent for teaching, and I decided to pursue it as a career. Currently, I provide mathematics classes for students from sixth to twelfth for all boards, including ICSE, CBSE, and West Bengal. I teach offline and online classes, each lasting for one and a half hours. I use interactive tools such as Zoom, Pentab, and One Note to make my lessons engaging and interactive for my students. To help my students excel in mathematics, I provide them with reference books, notes, and in-built assignments to test their knowledge. I also conduct monthly tests to assess their progress and identify improvement areas. Teaching on UrbanPro has allowed me to interact with students from different parts of the country and help them realise their full potential in mathematics. I want to continue making a positive impact in the lives of my students and help them develop a love for mathematics, just like I did

Aaa Mukherjee

Avishake Sir is an exceptional maths teacher! Engaging, patient, and effective. He break down complex concepts into easy-to-understand bits , provide individual attention and boost confidence. Highly recommended!"

Skills: Mathematics
Also teaches: Class 8 Tuition, Class 6 Tuition and more

(25)
superTutorSuper Tutor
locationImg Rohini Sector-24, Delhi
20 yrs of Exp 10 students
greenClock 1395 hrs of classes completed
rsIcon 450 per hour
Experienced Maths teacher with more than 20 years of experience.
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I am a teacher and I have been teaching for the past 20 years. l am presently teaching in a school. l have done MSc in Maths and have taught many students.

Amit Kumar

Thanks Ma'am for supporting Anvi in the subject. She has been getting more comfortable and relaxed with the theory and concepts in mathematics. Her fear is waning away and she shows an increased interest in the subject. I will definitely recommend you to all prospective parents. Thanks again!

Skills: Mathematics , Physics and more
Also teaches: Class 10 Tuition, Class 7 Tuition and more

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Other Subjects in CBSE - Class 9


FAQ

What is the meaning of Combination of solids?

It refers to a specific mathematical method or property in Surface Area and Volumes used to solve problems involving Combination of solids.

Why is Combination of solids important for CBSE - Class 9 exams?

This concept is crucial for the exams as questions related to Surface Area and Volumes and specifically Combination of solids are very common. It helps secure marks in the section effectively.

Is Combination of solids part of the latest NCERT syllabus?

Yes, Combination of solids is an integral part of the CBSE - Class 9 NCERT Mathematics syllabus. It is a key topic covered in the Surface Area and Volumes chapter.

What are common mistakes students make with Combination of solids?

Students often miss the minute details or fundamental definitions of Combination of solids. Regular revision and practice are needed to master the nuances.

How should I approach learning Combination of solids?

Start by understanding the formulas and logic, then practice applying them to simple problems. Solve the examples given in the NCERT textbook before moving to exercise problems.

How can UrbanPro help me understand Combination of solids better?

UrbanPro connects you with experienced Mathematics tutors who can explain Combination of solids with simple examples. You also get access to doubt-clearing sessions and mock tests for better preparation.

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