Co-ordinate Geometry Distance and Section Formula
- 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
- Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
- Areas of Sector and Segment of a Circle
- Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments
- Tangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection
- Tangent to a Circle
- Number of Tangents from a Point on a Circle
- 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 - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle
- Theorem: Angles in the Same Segment of a Circle Are Equal.
- Arc and Chord Properties - Angle in a Semi-circle is a Right Angle
- Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse
- Arc and Chord Properties - If Two Chords Are Equal, They Cut off Equal Arcs, and Its Converse (Without Proof)
- Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal
- Cyclic Properties
- Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers
Shares and Dividends
- Circumscribing and Inscribing a Circle on a Regular Hexagon
- Circumscribing and Inscribing a Circle on a Triangle
- Construction of Tangents to a Circle
- Circumference of a Circle
- Circumscribing and Inscribing Circle on a Quadrilateral
Ratio and Proportion
Gst (Goods and Services Tax)
- Sales Tax, Value Added Tax, and Good and Services Tax
- Computation of Tax
- Concept of Discount
- List Price
- Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST
- Basic/Cost Price Including Inverse Cases.
- Selling Price
- Goods and Service Tax (Gst)
- Gst Tax Calculation
- Gst Tax Calculation
- Input Tax Credit (Itc)
- Linear Inequations in One Variable
- Solving Algebraically and Writing the Solution in Set Notation Form
- Representation of Solution on the Number Line
- Arithmetic Progression - Finding Their General Term
- Sum of First ‘n’ Terms of an Arithmetic Progressions
- Simple Applications of Arithmetic Progression
- Median of Grouped Data
- Graphical Representation of Data as Histograms
- Ogives (Cumulative Frequency Graphs)
- Concepts of Statistics
- Graphical Representation of Data as Histograms
- Graphical Representation of Ogives
- Finding the Mode from the Histogram
- Finding the Mode from the Upper Quartile
- Finding the Mode from the Lower Quartile
- Finding the Median, upper quartile, lower quartile from the Ogive
- Calculation of Lower, Upper, Inter, Semi-Inter Quartile Range
- Concept of Median
- Mean of Grouped Data
- Mean of Ungrouped Data
- Median of Ungrouped Data
- Mode of Ungrouped Data
- Mode of Grouped Data
- Mean of Continuous Distribution
- Geometric Progression - Finding Their General Term.
- Geometric Progression - Finding Sum of Their First ‘N’ Terms
- Simple Applications - Geometric Progression
Co-ordinate Geometry Equation of a Line
- Slope of a Line
- Concept of Slope
- Equation of a Line
- Various Forms of Straight Lines
- General Equation of a Line
- Slope – Intercept Form
- Two - Point Form
- Geometric Understanding of ‘m’ as Slope Or Gradient Or tanθ Where θ Is the Angle the Line Makes with the Positive Direction of the x Axis
- Geometric Understanding of c as the y-intercept Or the Ordinate of the Point Where the Line Intercepts the y Axis Or the Point on the Line Where x=0
- Conditions for Two Lines to Be Parallel Or Perpendicular
- Simple Applications of All Co-ordinate Geometry.
- Surface area of a sphere
- Hollow Hemisphere
A sheet of paper , draw four circles with radius equal to the radius of the ball . Start filling the circles one by one , with the string you had wound around the ball in following fig.
The string, which had completely covered the surface area of the sphere, has been used to completely fill the regions of four circles, all of the same radius as of the sphere.
The surface area of a sphere of radius r = 4 times the area of a circle of radius r = 4 × `(π r^2)`
So, Surface Area of a Sphere = `4 πr^2`
where r is the radius of the sphere.
The curved surface area of a hemisphere is half the surface area of the sphere, which is `1/2` or `4πr^2`.
Curved Surface Area of a Hemisphere = `2πr^2`
Now taking the two faces of a hemisphere, its surface area` 2πr^2 + πr^2`
Total Surface Area of a Hemisphere = `3πr^2`
Shaalaa.com | Surface Area of a Sphere
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
The model of a building is constructed with the scale factor 1 : 30.
(i) If the height of the model is 80 cm, find the actual height of the building in meters.
(ii) If the actual volume of a tank at the top of the building is 27m3, find the volume of the tank on the top of the model.
The diameter of a sphere is 6 cm, It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm?
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and re casted into a single solid sphere. Taking π = 3.1, find the surface area of solid sphere formed.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.