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
Definition
- Cube: A cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex. The cube is the only regular hexahedron (i.e., a solid figure with six plane faces) and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
- Lateral surface area of the cube: Out of the six faces of a cube, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cube.
Formula
- Total surface area of the cube = 6a2.
- Lateral surface area of a cube = 4a2.
Notes
Cube:
A cube is a cuboid whose edges are all of equal length. A cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron (i.e., a solid figure with six plane faces) and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
Total surface area of cube:
Cube is a cuboid, whose length, breadth, and height are all equal.
Let, Length = breadth = height = a
Total surface area of the cube = 2(a × a + a × a + a × a)
Total surface area of the cube = 2 × (3a2)
Total surface area of the cube = 6a2
Lateral Surface area of cube:
Suppose, out of the six faces of a cube, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cube.
lateral surface area of a cube of side a is equal to 4a2.
Lateral surface area of a cube = 4a2.
Example
One side of a cubic box is 0.4 m. How much will it cost to paint the outer surface of the box at the rate of 50 rupees per sqm?
side = l = 0.4 m.
Total surface area of cube = 6 × (l)2
= 6 × (0.4)2
= 6 × 0.16
= 0.96 sqm
Cost of painting 1 sqm is 50 rupees.
∴ Cost of painting 0.96 sqm will be = 0.96 × 50 = 48 rupees
It will cost 48 rupees to paint the outer surface of the box.
