Topics
Number Systems
Real Numbers
Algebra
Pair of Linear Equations in Two Variables
- Linear Equations in Two Variables
- Graphical Method of Solution of a Pair of Linear Equations
- Substitution Method
- Elimination Method
- Cross - Multiplication Method
- Equations Reducible to a Pair of Linear Equations in Two Variables
- Consistency of Pair of Linear Equations
- Inconsistency of Pair of Linear Equations
- Algebraic Conditions for Number of Solutions
- Simple Situational Problems
- Pair of Linear Equations in Two Variables
- Relation Between Co-efficient
Arithmetic Progressions
Quadratic Equations
- Quadratic Equations
- Solutions of Quadratic Equations by Factorization
- Solutions of Quadratic Equations by Completing the Square
- Nature of Roots
- Relationship Between Discriminant and Nature of Roots
- Situational Problems Based on Quadratic Equations Related to Day to Day Activities to Be Incorporated
- Quadratic Equations Examples and Solutions
Polynomials
Geometry
Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Triangles
- Similar Figures
- Similarity of Triangles
- Basic Proportionality Theorem Or Thales Theorem
- Criteria for Similarity of Triangles
- Areas of Similar Triangles
- Right-angled Triangles and Pythagoras Property
- Similarity Triangle Theorem
- Application of Pythagoras Theorem in Acute Angle and Obtuse Angle
- Triangles Examples and Solutions
- Angle Bisector
- Similarity
- Ratio of Sides of Triangle
Constructions
Trigonometry
Heights and Distances
Trigonometric Identities
Introduction to Trigonometry
Statistics and Probability
Probability
Statistics
Coordinate Geometry
Lines (In Two-dimensions)
Mensuration
Areas Related to Circles
Surface Areas and Volumes
definition
- Volume: Amount of space occupied by a three-dimensional object is called its volume.
- Capacity: Capacity means the ability of the hollow object to hold substance, i.e., solid, liquid, or gas. It is a measure, that ascertains the amount of space available in a container, that can be filled with matter.
notes
Volume:
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The measure of this occupied space is called the Volume of the object.
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The volume of an object is the measure of the space it occupies, and the capacity of an object is the volume of substance its interior can accommodate.
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It is nothing but space, taken up by the substance which can be solid, liquid, or gas.
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Hence, the unit of measurement of either of the two is a cubic unit.
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Both solid and hollow objects have volume.
Capacity:
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Capacity means the ability of the hollow object to hold substance, i.e., solid, liquid, or gas. It is a measure, that ascertains the amount of space available in a container, that can be filled with matter.
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Measured in metric units such as liters, gallons, etc.
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Only hollow objects have the capacity.
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1 mL = 1 cm3,
1 L = 1000 cm3,
1 m3 = 1000000 cm3 = 1000 L.
