#### 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

- Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles
- Angle Sum Property of a Quadrilateral
- Types of Quadrilaterals
- Another Condition for a Quadrilateral to Be a Parallelogram
- Theorem of Midpoints of Two Sides of a Triangle
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Theorem: A Diagonal of a Parallelogram Divides It into Two Congruent Triangles.
- 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

##### 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

##### Mensuration

##### Areas - Heron’S Formula

##### Surface Areas and Volumes

##### Statistics and Probability

##### Statistics

##### Probability

#### 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 cm

^{3 }and the base area is 25 cm^{2}.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 m

^{3}?Volume of one box = 0.8 m

^{3}Volume of godown = 60 × 40 × 30 = 72000 m

^{3}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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