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Home  >  The Fundamental Unit of Life – Complete Guide For Class 9 Science Chapter 5

The Fundamental Unit of Life – Complete Guide For Class 9 Science Chapter 5

Welcome to iPrep, your Learning Super App. Our learning resources for the chapter,  The Fundamental Unit of Life in Science Class 9th Chapter 4 are designed to ensure that you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions and notes offer you the best of integrated learning with interesting explanations and examples.

The concept of “The Fundamental Unit of Life” in Class 9 explores the basic building blocks of all living organisms—the cell. Understanding cells is crucial as they are the smallest unit of life, and all biological activities are carried out within them. Cells form the basis of structure and function in every living organism, acting as the fundamental units that contribute to the organism’s overall health, growth, and reproduction. By delving into the intricacies of cell structure and function, students can appreciate how these tiny units work together to form complex tissues, organs, and systems that sustain life. This chapter lays a foundation for understanding more advanced biological concepts and the incredible diversity of life forms on our planet.

 What is a Cell?

Cells are the structural and functional units of life. Every living organism, from the smallest bacterium to the largest whale, is made up of cells. Cells can exist independently as single-celled organisms or as part of a larger multicellular organism.

Discovery of the Cell

The discovery of the cell was made possible by the invention of the microscope. Robert Hooke first observed cells in a cork slice in 1665, and Anton van Leeuwenhoek later observed living cells.

a visual representation of the first version of the microscope invented by Robert Hooke from class 9 science chapter 5 - the fundamental unit of life
a visual representation of living cells observed with a microscope from class 9 science chapter 5 The fundamental unit of life

Types of Cells

Prokaryotic Cells

  • Characteristics: Prokaryotic cells are simple, single-celled organisms without a defined nucleus. Their genetic material is free-floating within the cell.
  • Examples: Bacteria and Archaea.

Eukaryotic Cells

  • Characteristics: Eukaryotic cells are more complex and can be single-celled or multicellular. They have a defined nucleus that houses their genetic material.
  • Examples: Plants, animals, fungi, and protists.
a visual representation of animal cells from class 9 science chapter 5 The fundamental unit of life
a visual representation of plant cells from class 9 science chapter 5 The fundamental unit of life

Cell Structure

Cell structure directly exemplifies the fundamental unit of life, as each component such as –

Cell Membrane

  • Function: The cell membrane is a protective barrier that regulates what enters and exits the cell. It maintains the cell’s integrity and provides a controlled environment for cellular activities.

Cytoplasm

  • Function: The cytoplasm is a gel-like substance inside the cell membrane that contains all the cell’s organelles. It is the site for most cellular activities.

Nucleus

  • Function: The nucleus acts as the control center of the cell, containing the cell’s DNA and coordinating activities such as growth, metabolism, and reproduction.

Organelles

a visual representation of organelles from class 9 science chapter 5 The fundamental unit of life
  • Mitochondria: Known as the powerhouse of the cell, mitochondria generate energy through cellular respiration.
  • Ribosomes: These are the sites of protein synthesis.
  • Endoplasmic Reticulum (ER): The ER is involved in protein and lipid synthesis. It comes in two types: rough (with ribosomes) and smooth (without ribosomes).
a visual representation of Endoplasmic Reticulum from class 9 science chapter 5 The fundamental unit of life
  • Golgi Apparatus: It modifies, sorts, and packages proteins and lipids for storage or transport out of the cell.
  • Lysosomes: These contain enzymes that digest cellular waste and foreign material.
  • Chloroplasts: Found in plant cells, they are the sites of photosynthesis.

Cell Division: Cell division is a crucial concept in understanding “The Fundamental Unit of Life,” as it explains how cells reproduce, grow, and repair tissues. Cell division occurs as –

Mitosis

  • Function: Mitosis is a type of cell division that results in two daughter cells, each having the same number and kind of chromosomes as the parent nucleus. It is essential for growth and repair.

Meiosis

  • Function: Meiosis is a type of cell division that reduces the chromosome number by half, resulting in four daughter cells. It is crucial for sexual reproduction and genetic diversity.

Differences Between Plant and Animal Cells

Plant and animal cells both serve as the fundamental units of life, but they differ in key structures –

  • Plant Cells: Have a rigid cell wall, chloroplasts for photosynthesis, and a large central vacuole.
  • Animal Cells: Lack a cell wall and chloroplasts but have smaller vacuoles and more lysosomes.
a visual representation of Differences Between Plant and Animal Cells from class 9 science chapter 5 The fundamental unit of life

This comprehensive guide on “The Fundamental Unit of Life” offers an in-depth exploration of the fundamental building blocks of all living organisms, the cells. It delves into the intricate structure and diverse functions of cells, emphasizing their role as the smallest units of life. Through this chapter, students gain a deeper understanding of how cells operate, interact, and contribute to the complex processes that sustain life, laying the groundwork for more advanced studies in biology and life sciences.

In conclusion, this comprehensive guide on Class 9 Science Chapter 5 – The Fundamental Unit of Life has provided you with a detailed exploration of the essential building blocks of all living organisms—cells. By understanding the structure and functions of cells, including the differences between prokaryotic and eukaryotic cells, the intricacies of cell organelles, and the processes of cell division, you can appreciate how these fundamental units contribute to the complexity of life.

The chapter The Fundamental Unit of Life not only introduces you to the basic concepts of cell biology but also sets the stage for more advanced topics in biology. By mastering the details of The Fundamental Unit of Life, you prepare yourself for future studies and gain a deeper understanding of the living world.

With the help of iPrep’s engaging resources, including animated videos and practice questions, you can enhance your grasp of The Fundamental Unit of Life and excel in your studies. Embrace this knowledge as it forms the core foundation of all biological sciences and paves the way for further exploration into the diverse and fascinating world of life sciences.

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Home  >  Surface Areas and Volumes- Complete Guide For Class 9 Math Chapter 11

Surface Areas and Volumes- Complete Guide For Class 9 Math Chapter 11

Our learning resources for Mathematics Class 9 ‘Surface Areas and Volumes’ chapter 11 are designed to ensure that you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions, and notes offer you the best of integrated learning with interesting explanations and examples.

Our comprehensive approach ensures that you have access to everything you need to have an in-depth understanding of the chapter Surface Areas and Volumes. From detailed notes to interactive exercises, our materials are tailored to meet your learning needs and help you excel in your studies. Get ready to dive into an enriching educational experience that will make mastering this chapter a breeze.

Chapter 11, “Surface Area and Volume,” introduces students to calculate the surface area and volume of various 3D shapes, including cubes, cuboids, cylinders, cones, spheres, and hemispheres. It covers the derivation of formulas and practical applications. Emphasis is on understanding and applying these formulas to solve real-world problems, enhancing spatial reasoning and mathematical modeling skills.

Welcome to the fascinating world of 3-dimensional geometry! In this chapter, we explore solid figures, including cuboids, cubes, cylinders, cones, and spheres, learning how to calculate their surface areas and volumes. By mastering these concepts, you’ll be able to solve real-life problems involving various geometrical shapes.

Introduction to Solid Figures

Until now, we have focused on plane figures like circles, squares, and rectangles. Now, we shift our attention to solid figures, which have three dimensions. Examples include cuboids, cubes, and cylinders. Let’s delve into the formulas for their surface areas and volumes.

a visual illustration of solid shapes from the class 9 math chapter 11 - Surface Areas And Volumes

Surface Area of Cuboids and Cubes

Cuboid: A solid figure bounded by six rectangular plane regions.

a visual representation of area of cubes and cuboids from class 9 math chapter surface areas and volumes
  • Faces: Six rectangular faces.
  • Edges: Twelve edges where adjacent faces meet.
  • Lateral Faces: Four faces that meet the base of the cuboid.

Total Surface Area of a Cuboid: TSA = 2(lb+bh+lh)

 Lateral Surface Area of a Cuboid: LSA = 2(l+b)h

Cube: A cuboid with equal length, breadth, and height. 

image 313

Total Surface Area of a Cube: TSA = 6a²

Lateral Surface Area of a Cube: LSA = 4a²

Examples

  1. Cuboid Tiffin Box: Find the surface area for dimensions 16 cm x 8 cm x 6 cm. 
image 307

Solution: TSA = 2(16×8+8×6+6×16) = 2 ×272 = 544 cm²

  1. Dimensions Ratio: A cuboid with a surface area of 88 m² and dimensions in a 1:2:3 ratio. Find the dimensions of the cuboid.

Solution: The length, breadth, and height are l, 2l, and 3l respectively.

Then T.S.A of the cuboid = 2(lb+bh+hl)

88 = 2(lx2l + 2lx3l + lx3l)

88 = 2(2l² + 6l² + 3l²)

l² = 4

l = 2

Thus the dimensions are 2m, 4m, 6m.

Cylinder

A cylinder is formed by rolling a rectangular sheet.

image 316

Curved Surface Area (CSA): CSA = 2πrh

Total Surface Area: TSA = 2πr(r+h)

Examples

  1. Rectangular Sheet to Cylinder: A rectangular sheet of paper 44 cm x 18 cm is rolled along its length and a cylinder is formed. Find the radius of the cylinder.

Solution: The length of the rectangular sheet forms the circumference of the base, and the breadth becomes the height of the cylinder.

image 306

             2πr = 44

             2 × 22/7 × r = 44

             r = 44 × 7 /2 × 22 = 7 cm

  1. Hot Water Heating System: In a hot water heating system, there is a cylindrical pipe of length 28 m and the diameter is 5 cm. Find the total radiating surface in the system.

Solution: The total radiating surface = 2πrh

Length = height = 28 m

radius = 5 cm = 5/200 m

Therefore the curved surface area = 2 × 22/7 × 5/200 × 28 = 4.4 m²

Cones

A cone is formed by rotating a right-angled triangle around one of its legs.

image 309

Curved Surface Area: CSA = πrl

Total Surface Area: TSA = πr(l+r)

Examples

  1. Curved Surface Area: The radius of a cone is 3 cm and its vertical height is 4 cm. Find the area of its curved surface.

Solution: We have radius = 3 cm and h = 4 cm . Let l be the slant height of the cone

image 315

l ² = r² + h²

l² = 3² + 4²

l² = 9 + 16

l² = 25

l = 5

Therefore Curved surface area = πrl = 22/7 × 3 ×4 = 141.3 cm²

  1. Cloth for Conical Tent: How many meters of cloth 5 m wide will be required to make a conical tent, the radius of whose base is 7 m and whose height is 24 m?

Solution: According to the question 

image 320

l² = r² + h²

l² = 7² + 24²

l² = 49 + 576

l² = 625

l = 5

Area of the cloth = Curved surface area of the tent

l × b = πrl

l × 5 = 22/7 × 7 × 25

l =  110m

Spheres and Hemispheres

Sphere Surface Area: SA = 4πr²

image 317

Hemisphere Curved Surface Area: CSA = 2πr²

image 319

Total Surface Area of Hemisphere: TSA = 3πr²

Volumes of Solid Shapes

The space occupied by a solid object is its volume. For hollow objects, the capacity is measured.

image 311

Cuboid and Cube

image 312

Volume of a Cuboid: V = l × b × h

Volume of a Cube: V = a³

Cylinders

image 318

Volume of a Cylinder: V = πr²h

Hollow Cylinder: V = πh(R²−r²)

Cones

image 314

Volume of a Cone: V = 1/3πr²h 

Suppose there is a cone and a cylinder of the same height and the same radius.

The volume of the cone = 1/3 × Volume of the cylinder

V = 1/3πr²h

Sphere and Hemisphere

image 308

Volume of Sphere = 4/3 × πr³

Volume of Hemisphere = 2/3 × πr³

Understanding surface areas and volumes is crucial for solving practical problems involving three-dimensional shapes. By mastering these formulas and concepts, students can effectively tackle various geometrical challenges.

In conclusion, Chapter 11 – Surface Areas and Volumes of Class 9 Mathematics provides a thorough exploration of three-dimensional geometry. By understanding the key concepts and formulas for calculating the surface areas and volumes of various solid figures such as cuboids, cubes, cylinders, cones, spheres, and hemispheres, students gain valuable skills applicable to both academic and real-world scenarios.

Our resources for Surface Areas and Volumes ensure a comprehensive learning experience. With engaging animated videos, detailed notes, and practice questions, you will be well-equipped to master this chapter with ease. Whether you’re preparing for exams or seeking to reinforce your understanding, our materials are designed to enhance your grasp of Surface Areas and Volumes and help you excel in your studies.

By delving into the principles of Surface Areas and Volumes, you will improve your spatial reasoning and problem-solving abilities. Remember, mastering these concepts opens doors to tackling more complex geometrical problems, making your mathematical journey both enriching and rewarding. So, embrace the challenge and enjoy the learning process as you explore the fascinating world of Surface Areas and Volumes.

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Home  >  Lines and Angles – Complete Guide For Class 7 Math Chapter 5

Lines and Angles – Complete Guide For Class 7 Math Chapter 5

Welcome to iPrep, your Learning Super App. Our learning resources for the chapter, Lines and Angles in Mathematics for Class 7th are designed to ensure that you grasp this concept with clarity and perfection. Whether you’re studying for an upcoming exam or strengthening your concepts, our engaging animated videos, practice questions and notes offer you the best of integrated learning with interesting explanations and examples. 

The chapter on Lines and Angles introduces the fundamental concepts of geometry, essential for understanding the relationships between different geometric shapes and their properties. Students learn to identify and classify various types of angles, such as acute, right, obtuse, straight, and reflex angles, and understand how they are measured. This chapter emphasizes the importance of recognizing angle pairs, including complementary, supplementary, adjacent, and vertically opposite angles, and how these pairs interact when intersected by a transversal. Mastery of these concepts is critical for tackling more advanced geometric problems in higher-level mathematics and applying these skills to real-life situations, such as in architecture, engineering, and design.

Lines and Angles

There are various basic definitions covered in the chapter lines and angles, which include:

Point

A point is a precise location or position in a geometric space. It is an exact position but has no length, width, or thickness. Points are usually denoted by capital letters such as A, B, or C.

  • Example: Point A is a specific location on a plane.

Line

A line is a straight one-dimensional figure that extends infinitely in both directions. It has no endpoints and is often represented by a line with two arrowheads indicating that it continues indefinitely.

  • Example: Line AB extends infinitely in both directions through points A and B.

Line Segment

A line segment is a part of a line that is bounded by two distinct endpoints. It has a definite beginning and end, and it includes all the points between these endpoints.

  • Example: Line segment CD is the part of the line that starts at point C and ends at point D.

Angles

An angle is formed when two line segments or two rays have a common end-point.

Examples of Angles:

A visual representation of Lines and angles with an example of a chair and how we sit on it

Types of Angles

Within the chapter lines and angles, there is mention of various types of angles which include:

  • Acute Angle: An acute angle is less than 90°.
  • Right Angle: A right angle is exactly 90°.
  • Obtuse Angle: An obtuse angle is greater than 90° but less than 180°.
  • Straight Angle: A straight angle is exactly 180°.
  • Reflex Angle: A reflex angle is between 180° and 360°.
an illustration of the types of angles

Measurement of an Angle

Within the chapter lines and angles, we also get to learn the concept of measurement of an angle. So here is how yo measure and angle:

an example of the unit of an angle which is called Degree

Related Angles

Within the chapter lines and angles, we also get an understanding of Related angles. Some types of related angles include:

Complementary Angles

When the sum of measures of two angles is 90°, they are called complementary angles.

Example of Complementary Angles: In all sets, the sum of angles is 90°, making them complementary.

a visual of complementary angles which are another example of related angles from math class 7th chapter 5 - Lines and Angles

Supplementary Angles

When the sum of measures of two angles is 180°, they are called supplementary angles.

Example of Supplementary Angles: In all sets, the sum of angles is 180°, making them supplementary.

a visual of supplementary angles which are another example of related angles from math class 7th chapter 5 - Lines and Angles

Adjacent Angles

At vertex O, a pair of angles are placed next to each other.

Characteristics:

  • They have a common vertex.
  • They have a common arm.
  • The non-common arms are on either side of the common arm.

Example of Adjacent Angles: In all angles, one common vertex has several angles placed next to each other. So all these angles are adjacent angles

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Linear Pair

A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.

Example of Linear Pair:

a visual of linear pair which are another example of related angles from math class 7th chapter 5 - Lines and Angles

Vertically Opposite Angles

When two angles are formed by two intersecting lines, lying on opposite sides of the point of intersection, it is called vertically opposite angles.

Example of Vertically Opposite Angles: A pair of vertically opposite angles are: 

  • Angle AOX and Angle YOB. 
  • Angle AOY and angle XOB. 
a visual of vertically opposite angles which are another example of related angles from math class 7th chapter 5 - Lines and Angles

Pair of Lines

The chapter 5- “lines and angles” also covers the concept of Pair of Lines. Some examples of pairs of lines include:

Intersecting Lines

Intersecting lines are two or more lines that meet or cross each other at a single point. This point of intersection is where the lines share exactly one common point.

Examples:

  • The letter “X” is formed by two intersecting lines. These lines meet at a single point in the middle of the letter.       
  • The blades of a pair of scissors are two lines that intersect at the pivot point. As the blades open and close, they continue to intersect at this single point.

Transversal

A line that intersects two or more lines at distinct points is called a transversal.

Example of Transversal: Line ‘o’ intersecting lines L, M, N at distinct points 1, 2, 3. Thus, line “o” is a transversal.

a visual of transversal which is another example of intersecting lines from math class 7th chapter 5 - Lines and Angles

Angles Made by a Transversal: When lines l and m are cut by transversal p, eight angles are formed, each with a special name.

Table of Angles

a table having a list of all the angles made by a transversal.

Transversals of parallel lines give rise to quite interesting results. 

a visual example of Transversals of parallel lines

Corresponding Angles: If two parallel lines are cut by a transversal, each pair of corresponding angles is equal.

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Alternate Interior Angles: If two parallel lines are cut by a transversal, each pair of alternate interior angles is equal.

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Pair of Supplementary Angles: If two parallel lines are cut by a transversal, each pair of interior angles on the same side of the transversal are supplementary.

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Checking for Parallel Lines:

To determine if two lines are parallel: If a transversal gives rise to pairs of equal corresponding angles, equal alternate interior angles, and supplementary interior angles on the same side, then the lines are parallel.

         Examples: 

  • When a transversal “L” cuts two lines A and B, and angle 1 equals angle 2, lines A and B are parallel.
AD 4nXcc64UcO9QhE7HlW7EhVH23 7TP6ri9n1 sq9j6ytFMWs3iw5e5VVk1C61DPjpgSpzpORblrH4
  • When a transversal cuts two lines such that pairs of alternate interior angles are equal, the lines are parallel.
AD 4nXfG0zEV QLzwl2Pe4H1UBbDDHJXFnXP8 SugU QR MKEipTrc
  • When a transversal cuts two lines such that pairs of interior angles on the same side of the transversal are supplementary, the lines are parallel.
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In conclusion, the chapter on Lines and Angles provides a crucial foundation in geometry and iPrep’s resources on CLass 7th math Chapter 5 – Lines and Angles are designed to make mastering these concepts both engaging and effective. From understanding different types of angles to exploring their relationships and properties, our animated videos, practice questions, and notes offer a comprehensive approach to learning. By leveraging these tools, you’ll not only prepare for exams with confidence but also gain valuable skills applicable to various real-world scenarios. Dive into the chapter Lines and Angles with iPrep and strengthen your grasp of geometry for future academic success.

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