Introduction to algebra formulas for volume

Introduction to algebra formulas for volume

Algebra is one of the ancient syllabuses in Mathematics. Modern algebra is very much different from ancient algebra. Algebra is the subdivision of mathematics in which variables and numbers are used to express the equation.In algebra, variables are sometimes used in place of numbers. Algebra uses the property of commutative and associative property.  In algebra exams a variable is a symbol that represents a number. Algebra exams are mainly covers the linear equations, factorization, and polynomial equations.

Algebaric Geometry Formulas for Volume

There is more number of shapes in algebraic geometry. The geometry shapes are square, rectangle, triangle, prism, cylinder and cone, etc.. some of the volume formulas for geometry shapes are given below.

Application of algebraic geometry:

 1) Statistics

 2) Control theory

 3) Robotics

 4) Geometric modeling

 5) Game theory

Formulas for volume:

Formula fro volume of the cylinder:

      Volume = pi * r^2 * h. Here Pi = 3.14, r = radius, h = height.

Formula for volume of cube:

     Volume = a3. Here, a = side length of the cube.

Formula for volume of Sphere:

   Volume = (4/3) * pi * r^3. Here, pi =3.14, r = radius.

Algebra Formulas for Volume

Formula for volume of the Rectangular prism:

        Volume = a1 * a2 * a3. Here, a1 = Side 1, a2 = Side 2, a3 = Side 3.

Formula for volume of the cone:

       Volume = (1/3) * Pi * r^2 * h. Here, Pi = 3.14, r = Radius, h = Height.

Volume of the pyramid:

       Volume = (1/3) * base area * h.

Here, h = height, Base area = Depends on the base of the pyramid.

Formula for volume of the Ellipsoid:

      Volume = (4/3) * pi * r^1 * r^2 * r^3.

Here, Pi= 3.14, r1 = Radius , r^2 = Radius 2, r^3 = Radius 3.

Example Problems on Algebra Formulas for Volume

Ex 1:

Find the volume of cube with the side length is 5 cm.

Sol:

Given, side length a = 5 cm

              Volume of cube = a3

                                       = 53

                                       = 125 cm^3

Answer :

The final answer is 125 cm^3

Ex 2:

Find the volume of cylinder with the radius is 4 cm and height is 7 cm.

Sol:

Given, radius r = 4 cm, height h = 7 cm

          Volume of cylinder = pi * r^2 * h

                                            = 3.14 * 42 * 7 cm^3

                                            = 352 cm^3

Answer:

The final answer is 352 cm^3

Ex 3:

Find the volume of sphere with the radius is 12 cm.

Sol:

Given radius r = 12 cm

  Volume of sphere = (4 / 3) * pi * r^3

                            = (4 / 3) * pi * 123 cm^3

                            = 7234.56 cm^3

Answer:

The final answer is 7234.56 cm^3