#### Topics

##### Number Systems

##### Number Systems

##### Algebra

##### Polynomials

##### Linear Equations in Two Variables

##### Coordinate Geometry

##### Geometry

##### Coordinate Geometry

##### Mensuration

##### Introduction to Euclid’S Geometry

##### Lines and Angles

- Introduction to Lines and Angles
- Basic Terms and Definitions
- Intersecting Lines and Non-intersecting Lines
- Parallel Lines
- Pairs of Angles
- Parallel Lines and a Transversal
- Lines Parallel to the Same Line
- Angle Sum Property of a Triangle

##### Statistics and Probability

##### 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

##### 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

##### 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

## 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 = 6a
^{2}. - Lateral surface area of a cube = 4a
^{2}.

## 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 × (3a^{2})

**Total surface area of the cube = 6a ^{2 }**

**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 4a^{2}.

**Lateral surface area of a cube = 4a ^{2}.**

## 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.