volume of a cube formula

Let us learn about volume of a cube formula

Cube is one of the basic three dimensional images. Cube consists of six faces and each face meets at right angles. In total, cube has eight vertices's and twelve edges. As cube consists of six faces, it is also known as regular hexahedron. Volume is to be calculated for three dimensional images. Volume cube calculator is used to calculate the volume of cube in online. This calculator is very helpful for calculating the volume of cube. When the required values are entered in the calculator, it automatically generates the output.

Formula 1:

The formula for calculating the volume of a cube if all the sides are equal,
Volume of a cube = a³
Where, “a” is the side of the cube.
Formula 2:
Formula for calculating the volume of cube, when all the sides are different,
Volume of cube = l*w*h
where, l = length
w = width and
h = height

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pythagoras theorem proof

Let us learn about pythagoras theorem proof


In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).
It can be expressed in equation form as,
a² + b² = c²
Where, a and b are the sides of a right triangle
c is the hypotenuse of the right triangle

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orthographic drawing

Let us learn about orthographic drawing

A projection on a plane, using lines perpendicular to the plane

Graphic communications has many forms. Orthographics is one such form. It was developed as a way of communicating information about physical objects. It is part of a universal system of drawings. House plans - one well known drawing format, are a form of othographic projection. In simple terms, orthographic drawings are views (front, side, top, and so on) of an object. An orthographic view is only one side. It takes several views to show all the object. Before getting to views, it is useful to look at another type of drawing. Pictorial drawings show several sides at the same time. Many people find pictorial drawings easier to understand. They do not provide as much information as orthographic views. The most commonly used pictorial drawing for technical information is called isometric drawings. Isometric drawings were developed to approximate perspective, but are much easier to draw. For a square box, all the sides are drawn as vertical lines, or at 30 degrees to the horizontal.

Match the orthographic drawing to the isometric drawing.

A ) Figure 4
B ) Figure 2
C ) Figure 3
D ) Figure 1

Steps to derive

1 An orthographic drawing shows the top view, front view and right-side view of a three-dimensional figure.
2 Develop a three-dimensional figure from the orthographic views.
3 Top view forms the base of the structure. A three-dimensional structure is developed from the orthographic views.
4 Figure 2 gives the isometric drawing of the structure developed from orthographic drawing.

Hence the right answer is Option B

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least squares regression line

Let us learn about least squares regression line

Regression is the measure of the average relationship between two or more variables in terms of the original units of the data. This can be represented by an equation of a straight line which can be obtained by the method of least squares. The equations are of two forms as y on x and x on y. To obtain them we use the following normal equatons.

(i) Regression line y on x: It is given by y = hx + k.

Their normal equations are:

Σy = hΣx + nk ……………… (1)

Σxy = hΣx ² + kΣx …………. (2)

By solving (1) and (2), we arrive at the required equation y = hx + k

(ii) Regression line x on y: It is given by x = hy + k.

Their normal equations are:

Σx = hΣy + nk ……….. (1)

Σxy = hΣy ² + kΣy ………… (2)

By solving (1) and (2), we arrive at the required equations x = hy + k

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plot line

Let us learn about plot line

A line plot is defined as a graph that shows frequency of data along a number line. It is best to use a line plot when comparing fewer numbers.

• A line plot shows data on a number line with the symbol x or other marks to show frequency.

• In the applications of line plot, we have also created the scatter plot analysis. I we go in the wrong path or plotting the extra values or plotting the values in different place or leaving some values when we plotting make great difference in the diagrams.

Line Plot Maker - Making a Number Line Plot:

• To define the scale which we use, if the data is described as 100 the scale is increased by 10. So that we define the scale as 10 for 100

• Next we have to draw the horizontal line to across the paper.

• Break the grid as per the required scale.

• Place the data values of x in the x-axis and y in the y-axis.

X

X X

X X X

X X X X X X

0 1 2 3 4 5 6 7 8 9 10

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fraction reducer

Let us learn about fraction reducer

The word fraction has been derived from the Latin word fractus, means broken

A Fraction means a part of a group or a region or a whole.

Fractions having the same(common) denominators but different numerators are known as like fractions.

Fraction is defined as an element of quotient field. Fraction can be represented as " a / b " here fraction variable 'a' denotes the value called as numerator and fraction variable 'b' denotes the value called as denominator and the denominator 'b' is not equal to zero.

Fractional functions:

The fraction rule is used in following functions,

1. Addition
2. Subtraction
3. Multiplication
4. Division

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change of base formula

Let us learn about "change of base formula"

The solving change of base formula is known as formulas which it permits us to rework a logarithm by means of the logs that may be is written with different base.

The change of base formula is given by,

Log _a x = log _b x / log _b a

Here, assume that a, b and x are positive where a≠1 and b≠1.

Problem

Solve log ₁₆ 32

Change of base formula => log_a x = log_bx / log_ba

log ₁₆ 32 = log ₂ 32 / log ₂ 16

= 5 / 4

Thus a formula that allows you to rewrite a logarithm in terms of logs written with another base. This is especially helpful when using a calculator to evaluate a log to any base other than 10 or e.

In our next blog we shall learn "how to simplify radicals"

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