Topics
Number Systems
Number Systems
Polynomials
Algebra
Algebraic Expressions
Algebraic Identities
Coordinate Geometry
Linear Equations in Two Variables
Coordinate Geometry
Geometry
Area
Constructions
- Introduction of Constructions
- Geometric Constructions
- Some Constructions of Triangles
Introduction to Euclid’S Geometry
Mensuration
Statistics and Probability
Lines and Angles
- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Concept of Pairs of Angles
- Concept of Transversal Lines
- Basic Properties of a Triangle
Probability
Triangles
Quadrilaterals
- Properties of Quadrilateral
- 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
Circles
Areas - Heron’S Formula
- Area of a Triangle by Heron's Formula
- Application of Heron’s Formula in Finding Areas of Quadrilaterals
- Geometric Interpretation of the Area of a Triangle
Surface Areas and Volumes
Statistics
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 cm3 and 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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