Topics
Compound Interest
- Compound Interest as a Repeated Simple Interest Computation with a Growing Principal
- Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years
- Use of Formula
- Finding CI from the Relation CI = A – P
Commercial Mathematics
Goods and Services Tax (G.S.T.)
Banking
Algebra
Geometry
Shares and Dividends
Symmetry
Mensuration
Linear Inequations
Quadratic Equations
- Quadratic Equations
- Method of Solving a Quadratic Equation
- Factorisation Method
- Quadratic Formula (Shreedharacharya's Rule)
- Nature of Roots of a Quadratic Equation
- Equations Reducible to Quadratic Equations
Trigonometry
Statistics
Problems on Quadratic Equations
- Method for Solving a Quadratic Word Problem
- Problems Based on Numbers
- Problems on Ages
- Problems Based on Time and Work
- Problems Based on Distance, Speed and Time
- Problems Based on Geometrical Figures
- Problems on Mensuration
- Problems on C.P. and S.P.
- Miscellaneous Problems
Ratio and Proportion
Probability
Remainder Theorem and Factor Theorem
- Function and Polynomial
- Division Algorithm for Polynomials
- Remainder Theorem
- Factor Theorem
- Applications of Factor Theorem
Matrices
Arithmetic Progression
Geometric Progression
Reflection
- Co-ordinate Geometry
- Advanced Concept of Reflection in Mathematics
- Invariant Points
- Combination of Reflections
- Using Graph Paper for Reflection
Section and Mid-Point Formulae
Equation of a Line
Similarity
Loci
- Locus
- Points Equidistant from Two Given Points
- Points Equidistant from Two Intersecting Lines
- Summary of Important Results on Locus
- Important Points on Concurrency in a Triangle
Angle and Cyclic Properties of a Circle
Tangent Properties of Circles
Constructions
Volume and Surface Area of Solids (Cylinder, Cone and Sphere)
- Mensuration of Cylinder
- Hollow Cylinder
- Mensuration of Cones
- Mensuration of a Sphere
- Hemisphere
- Conversion of Solids
- Solid Figures
- Problems on Mensuration
Trigonometrical Identities
Heights and Distances
- Angles of Elevation and Depression
- Problems based on Elevation and Depression
Graphical Representation of Statistical Data
Measures of Central Tendency (Mean, Median, Quartiles and Mode)
Probability
- Definition: Cone
- Types of Cones
- Properties of a Cone
- Activity
CISCE: Class 10
Definition: Cone
The solid obtained on revolving a right-angled triangle about one of its sides (other than the hypotenuse) is called a cone or a right circular cone.
CISCE: Class 10
Formula: Cone
- Volume = \[\frac{1}{3}\pi r^2h\]
-
Curved (lateral) surface area = πrl or \[\pi r\sqrt{h^{2}+r^{2}}\]
(\[l=\sqrt{h^2+r^2}\]) -
Total surface area =
Structure and Types of Cones with Examples
Parts of a cone:
- Apex:
The pointed tip is at the top of the cone. - Curved Face:
The curved face is a smooth, rounded surface that extends from the base to the apex. - Circular Flat Face:
The flat, circular base is present at the bottom of closed cones. - Circular Edge:
This term refers to the line that separates the curved face from the circular base.
Types of Cone:
Closed Cone :
A closed cone consists of one curved face, one flat circular face, and one circular edge.
Example: Ice cream cone (closed)
Open Cone :
An open cone features a curved face and a circular edge, but it lacks a flat face.
Example: clown’s cap
Maharashtra State Board: Class 6
Activity
Making a Cone from a Circle
Steps:
- Draw a Circle:
Use a compass to draw a circle on paper with centre C.
- Mark Two Radii:
Draw two lines from Centre C to the edge of the circle, naming them CR and CS (these are the radii).
- Cut Along the Radii:
Cut the circle along both radii CR and CS to get two pieces.
- Form a Cone Shape:
Take one piece and bring together the sides (CR and CS).
Join them to form a cone shape.
Conclusion:
You get a cone from each piece of the circle by joining the two straight edges (radii).
Video Tutorials
Shaalaa.com | Volume of a Right Circular Cone
to track your progress
