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Number Systems
Number Systems
- Introduction of Real Number
- Concept of Irrational Numbers
- Real Numbers and Their Decimal Expansions
- Representing Real Numbers on the Number Line
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- Laws of Exponents for Real Numbers
Algebra
Polynomials
- Concept of Polynomials
- Polynomials in One Variable
- Zeroes of a Polynomial
- Remainder Theorem
- Factorising the Quadratic Polynomial (Trinomial) of the type ax2 + bx + c, a ≠ 0.
Linear Equations in Two Variables
- Linear Equations in Two Variables
- Linear Equation in One Variable
- Solution of a Linear Equation
- Graph of a Linear Equation in Two Variables
- Equations of Lines Parallel to the X-axis and Y-axis
Algebraic Expressions
- Algebraic Expressions
Algebraic Identities
- Algebraic Identities
Coordinate Geometry
- Coordinate Geometry
- Cartesian System
- Plotting a Point in the Plane If Its Coordinates Are Given.
Geometry
Introduction to Euclid’S Geometry
- Concept for Euclid’S Geometry
- Euclid’S Definitions, Axioms and Postulates
- Equivalent Versions of Euclid’S Fifth Postulate
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Concept of Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle
Triangles
- Concept of Triangles - Sides, Angles, Vertices, Interior and Exterior of Triangle
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Properties of a Triangle
- Some More Criteria for Congruence of Triangles
- Inequalities in a Triangle
Quadrilaterals
- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Another Condition for a Quadrilateral to Be a Parallelogram
- The Mid-point Theorem
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem : If Each Pair of Opposite Sides of a Quadrilateral is Equal, Then It is a Parallelogram.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.
- Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection)
- Theorem : If the Diagonals of a Quadrilateral Bisect Each Other, Then It is a Parallelogram
Area
- Concept of Area
- Corollary: A rectangle and a parallelogram on the same base and between the same parallels are equal in area.
- Theorem: Parallelograms on the Same Base and Between the Same Parallels.
- Corollary: Triangles on the same base and between the same parallels are equal in area.
Circles
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Angle Subtended by a Chord at a Point
- Perpendicular from the Centre to a Chord
- Circles Passing Through One, Two, Three Points
- Equal Chords and Their Distances from the Centre
- Angle Subtended by an Arc of a Circle
- Cyclic Quadrilateral
Constructions
- Introduction of Constructions
- Basic Constructions
- Some Constructions of Triangles
Mensuration
Areas - Heron’S Formula
- Area of a Triangle
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
Surface Areas and Volumes
- Surface Area of a Cuboid
- Surface Area of Cylinder
- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Volume of a Cuboid
- Volume of a Cylinder
- Volume of a Right Circular Cone
- Volume of a Sphere
Statistics and Probability
Statistics
- Concepts of Statistics
- Collecting Data
- Presentation of Data
- Graphical Representation of Data
- Measures of Central Tendency
Probability
- Probability - an Experimental Approach

formula

Volume of a Cuboid = l × b × h

notes

Volume of a Cuboid:

Volume of a Cuboid = Measure of the space occupied by the cuboid.

The area of the plane region occupied by each rectangle × height.

Volume of a Cuboid = base area × height = length × breadth × height.

Volume of a Cuboid = l × b × h, where l, b, and h are respectively the length, breadth, and height of the cuboid.

Example

Find the height of a cuboid whose volume is 275 cm³and the base area is 25 cm².

Volume of a cuboid = Base area × Height

Hence height of the cuboid = `"Volume of cuboid"/"Base area"`

=`275/25`

= 11 cm

Height of the cuboid is 11 cm.

Example

A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 m³?

Volume of one box = 0.8 m³

Volume of godown = 60 × 40 × 30 = 72000 m³

Number of boxes that can be stored in the godown = `"Volume of the godown"/"Volume of one box"`

= `(60 xx 40 xx 30)/(0.8)`

= 90,000

Hence the number of cuboidal boxes that can be stored in the godown is 90,000.

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Volume of a Cuboid

Topics

Number Systems

Number Systems

Algebra

Polynomials

Linear Equations in Two Variables

Algebraic Expressions

Algebraic Identities

Coordinate Geometry

Geometry

Introduction to Euclid’S Geometry

Lines and Angles

Triangles

Quadrilaterals

Area

Circles

Constructions

Mensuration

Areas - Heron’S Formula

Surface Areas and Volumes

Statistics and Probability

Statistics

Probability

formula

notes

Volume of a Cuboid:

Example

Example

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Volume of a Cuboid

Topics

Number Systems

Number Systems

Algebra

Polynomials

Linear Equations in Two Variables

Algebraic Expressions

Algebraic Identities

Coordinate Geometry

Geometry

Introduction to Euclid’S Geometry

Lines and Angles

Triangles

Quadrilaterals

Area

Circles

Constructions

Mensuration

Areas - Heron’S Formula

Surface Areas and Volumes

Statistics and Probability

Statistics

Probability

formula

notes

Volume of a Cuboid:

Example

Example

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