Volume of a Cube using formula

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of trigonal trapezohedron. The cube is dual to the octahedron. It has cubical symmetry (also called octahedral symmetry). A cube is the three-dimensional case of the more general concept of a hypercube.The volume of any solid, liquid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes such as square (geometry help) squares are assigned zero volume in the three-dimensional space. Volume is commonly presented in units such as cubic meters, cubic centimeters, litres, or millilitres.Let's see how to find the volume of a cube by using formula for volume
Question:-

If the edge of the cube is 10 m ,then what is the volume of the cube?

Answer:-

Given the edge as 10m

in a cube all the edges are same

so the length of the cube=10m

Width of the cube= 10m

height of the cube = 10m

Volume formula is

length x width x height

so the volume of the given cube is

10 x 10 x 10 = 30 m³

How to find the area of a quadrilateral

a quadrilateral is a polygon with four 'sides' or edges and four vertices or corners. Sometimes, the term quadrangle is used, for analogy with triangle, and sometimes tetragon for consistency with pentagon (5-sided), hexagon (6-sided) and so on. The word quadrilateral is made of the words quad and lateral. Quad means four and lateral means sides. The interior angles of a quadrilateral add up to 360 degrees of arc.Quadrilaterals are simple (not self-intersecting) or complex (self-intersecting). Simple quadrilaterals are either convex or concave.

Two identical isosceles triangles with side length 5 cm are joined at their bases with length 8 cm .What is the area of the quadrilateral.


a²+b²=c²

4²+b²=5²

16+b²=25

b²=25-16

b²=9

b=√9=3

Now by using area of triangle formula let's find the area of ABC ,which is
a part of the quadrilateral
Area of Δ ABC=1/2 (8)(3)

= 4*3=12 square units

Area of quadrilateral ABCD=12+12 =24 square units

How to find a mid point

Topic:-Mid point of a line joining

The midpoint is the middle point of a line segment. It is equidistant from both endpoints.

Here we have 2 points given which will result a line joining ,And we have to find the mid point for this line joining by using the mid point formula


Question:-

Find the midpoint of the line joining these points(3,9)(7,11).

Solution:-

Formula to find mid point:

   x1+x2          y1+y2
  --------      ----------
    2               2


     3+7                    9+11
   ------                  ---------
     2                        2



    10                     20
   -----                 -------
     2                     2


     5                    10

So (5,10) is the mid point.

Finding the inverse of a function

In relations and functions of math, there is concept of inverse function which is explained below using simple example.

Topic : Inverse of a function

function is always denoted by f and variable by x as f(x) and expression can be algebraic expression or trigonometric expressions.

Problem : Find the inverse of a function f(x) = 2x – 5

Solution :

f(x) = 2x – 5
Let y = f(x)
y = 2x – 5
Add 5 on both the sides of the equation
y + 5 = 2x
Now, divide by 2 on both the sides of the equation
(y+5)/2 = x