Topics
Rational and Irrational Numbers
- Rational Numbers
- Properties of Rational Numbers
- Decimal Representation of Rational Numbers
- Concept of Irrational Numbers
- Concept of Real Numbers
- Surds
- Rationalisation of Surds
- Simplifying an Expression by Rationalization of the Denominator
Compound Interest [Without Using Formula]
- Calculation of Interest
- Concept of Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Concept of Compound Interest
Compound Interest [Using Formula]
- Concept of Compound Interest
- Inverse Formula
- Miscellaneous Problem
- When the Interest is Compounded Half Yearly
- When the Time is Not an Exact Number of Years and the Interest is Compounded Yearly
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
Expansions
- Algebraic Identities
- Expansion of (a + b)3
- Expansion of Formula
- Special Product
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
Factorisation
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Taking Out Common Factors
- Factorisation by Grouping
- Factorisation of a Quadratic Trinomial by Splitting the Middle Term
- Method of Factorisation : Difference of Two Squares
- Method of Factorisation : the Sum Or Difference of Two Cubes
Simultaneous (Linear) Equations [Including Problems]
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Methods of Solving Simultaneous Linear Equations by Elimination Method
- Method of Elimination by Equating Coefficients
- Equations Reducible to Linear Equations
- Simultaneous method
- Methods of Solving Simultaneous Linear Equations by Cross Multiplication Method
- Simple Linear Equations in One Variable
- Introduction to linear equations in two variables
Indices [Exponents]
- Laws of Exponents
- Handling Positive, Fraction, Negative and Zero Indices
- Simplification of Expressions
- Solving Exponential Equations
Logarithms
- Introduction of Logarithms
- Interchanging Logarithmic and Exponential Forms
- Logarithmic to Exponential
- Exponential to Logarithmic
- Laws of Logarithm
- Product Law
- Quotient Law
- Power Law
- Expansion of Expressions with the Help of Laws of Logarithm
- More About Logarithm
Triangles [Congruency in Triangles]
- Concept of Triangles
- Relation Between Sides and Angles of Triangle
- Important Terms of Triangle
- Congruence of Triangles
- Criteria for Congruence of Triangles
Isosceles Triangles
- Classification of Triangles based on Sides- Equilateral, Isosceles, Scalene
- Isosceles Triangles Theorem
- Converse of Isosceles Triangle Theorem
Inequalities
- Inequalities in a Triangle
- If two sides of a triangle are unequal, the greater side has the greater angle opposite to it.
- If Two Angles of a Triangle Are Unequal, the Greater Angle Has the Greater Side Opposite to It.
- Of All the Lines, that Can Be Drawn to a Given Straight Line from a Given Point Outside It, the Perpendicular is the Shortest.
Mid-point and Its Converse [ Including Intercept Theorem]
- Theorem of Midpoints of Two Sides of a Triangle
- Equal Intercept Theorem
Pythagoras Theorem [Proof and Simple Applications with Converse]
Rectilinear Figures [Quadrilaterals: Parallelogram, Rectangle, Rhombus, Square and Trapezium]
- Introduction of Rectilinear Figures
- Names of Polygons
- Concept of Quadrilaterals
- Types of Quadrilaterals
- Diagonal Properties of Different Kinds of Parallelograms
- Property: The Opposite Sides of a Parallelogram Are of Equal Length.
- Property: The Opposite Angles of a Parallelogram Are of Equal Measure.
- Property: The diagonals of a rhombus are perpendicular bisectors of one another.
- Property: The Diagonals of a Rectangle Are of Equal Length.
- Property: The diagonals of a square are perpendicular bisectors of each other.
Construction of Polygons (Using Ruler and Compass Only)
- Constructing a Quadrilateral
- Construction of Parallelograms
- Construction of Trapezium
- Construction of a Rectangle When Its Length and Breadth Are Given.
- Construction of Rhombus
- Construction of Square
- To Construct a Regular Hexagon
Area Theorems [Proof and Use]
- Concept of Area
- Figures Between the Same Parallels
- Triangles with the Same Vertex and Bases Along the Same Line
Circle
- Concept of Circle
- Arc, Segment, Sector
- Chord Properties - a Straight Line Drawn from the Center of a Circle to Bisect a Chord Which is Not a Diameter is at Right Angles to the Chord
- Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof)
- Theorem: Equal chords of a circle are equidistant from the centre.
- Theorem : The Chords of a Circle Which Are Equidistant from the Centre Are Equal.
- Chord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line
- Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse
Statistics
- Concepts of Statistics
- Variable of Equation
- Tabulation of Data
- Frequency
- Frequency Distribution Table
- Frequency Distribution Table
- Class Intervals and Class Limits
- Cumulative Frequency Table
- Graphical Representation of Data
- Graphical Representation of Continuous Frequency Distribution
Mean and Median (For Ungrouped Data Only)
- Mean of Ungrouped Data
- Properties of Mean
- Concept of Median
Area and Perimeter of Plane Figures
Solids [Surface Area and Volume of 3-d Solids]
- Introduction of Solids
- Surface Area of a Cuboid
- Surface Area of a Cube
- Surface Area of Cylinder
- Cost of an Article
- Cross Section of Solid Shapes
- Flow of Water ( or any other liquid )
Trigonometrical Ratios [Sine, Consine, Tangent of an Angle and Their Reciprocals]
- Concept of Perpendicular, Base, and Hypotenuse in a Right Triangle
- Notation of Angles
- Trigonometric Ratios and Its Reciprocal
- Reciprocal Relations
Trigonometrical Ratios of Standard Angles [Including Evaluation of an Expression Involving Trigonometric Ratios]
- Trigonometric Ratios of Some Special Angles
- Trigonometric Ratios of Some Special Angles
- Trigonometric Equation Problem and Solution
- Trigonometric Ratios of Some Special Angles
Solution of Right Triangles [Simple 2-d Problems Involving One Right-angled Triangle]
- Solution of Right Triangles
Complementary Angles
- Complementary Angles
- Trigonometric Ratios of Complementary Angles
- Complementary Angles for Sine ( Sin ) and Cosine ( Cos )
- Complimentary Angles for Tangent ( Tan ) and Contangency ( Cot )
- Complimentary Angles for Secant ( Sec ) and Cosecant ( Cosec )
Co-ordinate Geometry
- Coordinate Geometry
- Dependent and Independent Variables
- Ordered Pair
- Cartesian Coordinate System
- Co-ordinates of Points
- Quadrants and Sign Convention
- Plotting of Points
- Graph
- Graphs of Linear Equations
- Inclination and Slope
- Y-intercept
- Finding the Slope and the Y-intercept of a Given Line
Graphical Solution (Solution of Simultaneous Linear Equations, Graphically)
Distance Formula
- Distance Formula
- Distance Formula
- Circumcentre of a Triangle
Profit , Loss and Discount
- Concept of Discount
- To Find C.P., When S.P. and Gain (Or Loss) Percent Are Given
- To Find S.P., When C.P. and Gain (Or Loss) Percent Are Given
- Profit or Loss as a Percentage
- Concept of Discount
- Overhead Expenses
Construction of Triangles
- Construction of Triangles
- Construct Isosceles Triangle
Changing the Subject of a Formula
- Changing the Subject of a Formula
Similarity
Formula
- Cuboid: A cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. A cuboid looks like a rectangular box. It has 6 faces. Each face has 4 edges. Each face has 4 corners (called vertices).
- Surface of a cuboid: the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying the length by breadth for each of them separately and then adding the six areas together.
- Lateral surface area of the cuboid: Out of the six faces of a cuboid, 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 cuboid.
Formula
- Total surface area of cuboid = 2(lb + bh + lh)
- The lateral surface area of a cuboid = 2h(l + b)
Notes
Cuboid:
A cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. A cuboid looks like a rectangular box. It has 6 faces. Each face has 4 edges. Each face has 4 corners (called vertices).
Total Surface Area of a Cuboid:
This Figure shows us that the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying the length by breadth for each of them separately and then adding the six areas together.
Let Consider h = height, b = breadth, l = length of cuboid
The total surface area of a cuboid is equal to the sum of all area of 6 rectangles.
Area of □ MNOP = Area of □ QRST = (l × b) cm2
Area of □ MRSN = Area of □ PQTO = (l × h) cm2
Area of □ MPQR = Area of □ NOTS = (b × h) cm2
Total surface area of cuboid = sum of all area of 6 rectangle = 2(l × b) + 2(b × h) + 2(l × h)
Total surface area of cuboid = 2(lb + bh + lh).
Lateral Surface area of cuboid:
Suppose, out of the six faces of a cuboid, 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 cuboid.
The lateral surface area of a cuboid is 2h(l + b), i.e., 2 × height × sum of length and breadth.
The lateral surface area of a cuboid = 2h(l + b).
Example
How much sheet metal is required to make a closed rectangular box of length 1.5 m, breadth 1.2 m, and height 1.3 m?
length of box = l = 1.5 m,
breadth = b = 1.2 m,
height = h = 1.3 m.
Surface area of box = 2 (l × b + b × h + l × h)
= 2 (1.5 × 1.2 + 1.2 × 1.3 + 1.5 × 1.3)
= 2 (1.80 + 1.56 + 1.95)
= 2 (5.31)
= 10.62 sqm
10.62 sqm of sheet metal will be needed to make the box.
Example
An aquarium is in the form of a cuboid whose external measures are 80 cm × 30 cm × 40 cm. The base, side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?
The length of the aquarium = l = 80 cm
Width of the aquarium = b = 30 cm
Height of the aquarium = h = 40 cm
Area of the base = l × b = 80 × 30 = 2400 cm2
Area of the side face = b × h = 30 × 40 = 1200 cm2
Area of the back face = l × h = 80 × 40 = 3200 cm2
Required area = Area of the base + area of the back face + (2 × area of a side face)
= 2400 + 3200 + (2 × 1200) = 8000 cm2
Hence the area of the coloured paper required is 8000 cm2.
Example
The internal measures of a cuboidal room are 12 m × 8 m × 4 m. Find the total cost of whitewashing all four walls of a room, if the cost of whitewashing is Rs. 5 per m2. What will be the cost of whitewashing if the ceiling of the room is also whitewashed.
Let the length of the room = l = 12 m
Width of the room = b = 8 m
Height of the room = h = 4 m
Area of the four walls of the room = Perimeter of the base × Height of the room
= 2 (l + b) × h = 2 (12 + 8) × 4
= 2 × 20 × 4 = 160 m2
Cost of white washing per m2 = Rs. 5
Hence the total cost of white washing four walls of the room = Rs. (160 × 5) = Rs. 800.
Area of ceiling is 12 × 8 = 96 m2
Cost of white washing the ceiling = Rs. (96 × 5) = Rs. 480
So the total cost of white washing = Rs. (800 + 480) = Rs. 1280
If you would like to contribute notes or other learning material, please submit them using the button below.
Shaalaa.com | Total Surface Area & Lateral Surface Area of a Cuboid
to track your progress
