Topics
Number Systems
Number Systems
Polynomials
Algebra
Coordinate Geometry
Linear Equations in Two Variables
Geometry
Coordinate Geometry
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
- Introduction to Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Angle Sum Property of a Triangle
Triangles
- Concept of Triangles
- 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
- Properties 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
Circles
Areas - Heron’S Formula
Surface Areas and Volumes
Statistics
Algebraic Expressions
Algebraic Identities
Area
Constructions
- Introduction of Constructions
- Basic Constructions
- Some Constructions of Triangles
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 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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