Trigonometry formulas for class 10

Trigonometry formulas for class 10

Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

Trigonometry is most simply associated with planar right-angle triangles (each of which is a two-dimensional triangle with one angle equal to 90 degrees). The applicability to non-right-angle triangles exists, but, since any non-right-angle triangle (on a flat plane) can be bisected to create two right-angle triangles, most problems can be reduced to calculations on right-angle triangles. Thus the majority of applications relate to right-angle triangles. One exception to this is spherical trigonometry, the study of triangles on spheres, surfaces of constant positive curvature, in elliptic geometry (a fundamental part of astronomy and navigation). Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.

Trigonometry formulas for class 10

Circles Class 9 Ncert Solutions

Circles Class 9 Ncert Solutions

Area Of Circle = pi * r^2
Circumference of Circle = 2 * pi * r

A circle is the set of all points equidistant from a given point. The point from which all the points on a circle are equidistant is called the center of the circle, and the distance from that point to the circle is called the radius of the circle. A circle is named with a single letter, its center.
All circles have a diameter, too. The diameter of a circle is the segment that contains the center and whose endpoints are both on the circle. The length of the diameter is twice that of the radius. Therefore, all diameters of a circle are congruent, too.

Keep in mind that an infinite number of radii and diameters can be drawn in a circle. Although they are all congruent, they are not the same. Sometimes a strategically placed radius will help make a problem much clearer. Likewise, diameters can be drawn into a circle to strategically divide the area within the circle. Each of these techniques is prevalent in geometric proofs, and each is based on the facts that all radii are congruent, and all diameters are congruent. However, their position when drawn makes each one different. 

Surface Area and Volume Class 9 and 10

Surface Area and Volume

Surface Area and Volume Class 9

Formulas for Volume :

Formulas for Surface area(Total surface area) :

The surface area is the area that describes the material that will be used to cover a geometric solid. When we determine the surface areas of a geometric solid we take the sum of the area for each geometric form within the solid.

Surface Area and Volume Class 10

The volume is a measure of how much a figure can hold and is measured in cubic units. The volume tells us something about the capacity of a figure.

The surface area of a solid object is a measure of the total area that the surface of an object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with flat polygonal faces), for which the surface area is the sum of the areas of its faces. Smooth surfaces, such as a sphere, are assigned surface area using their representation as parametric surfaces. This definition of surface area is based on methods of infinitesimal calculus and involves partial derivatives and double integration.

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.