LESSON ON VOLUME OF SOLIDS

Often, students work with shapes and solids under Geometry. Geometry deals with the study of solids and shapes and the measurements associated with them. Therefore various calculations with respect to the size, shape and volume is often done under Geometry. One of such computations is calculating volume of solids.
There are various types of solids. They are:

· Cube

· Cuboid

· Prism

· Pyramid

· Cylinder

· Sphere

· Cone

Students can use various volume formulas to calculate the volume of the various solids. The Volume is basically the 3 dimensional 'space' occupied by a particular solid.

Students can solve problems on finding volume and learn how to find volume of various solids. Ample problems are available online for students to practice upon. They can also get Geometry tutoring online to get help with solving problems in geometry.

how to find the slope

Let us learn how to find the slope

Interpret the slopes of the following lines joining

(i) (6,4) and (−7, 4) (ii) (−2,8) and (−2, 7).

(i) To find Slope of the given line “m”= y₂- y₁ / x₂ – x₁ = 4-4 / -7- 6 = 0 /-13 = 0

∴ Therefore line is parallel to the x-axis.

(ii) To find Slope of the given line “m” = y₂- y₁ / x₂ – x₁ = 7-8 / -2+2 = not defined.

Therefore, The line is perpendicular to the x-axis.

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final exam calculator

Let us learn about final exam calculator

Final exam score is referred as the calculation of the marks secured by each student that can be used to predict the results of the students & the grades secured by them.

Final exam score includes calculation of the total marks of students, calculation of the percentages & the final step is the prediction of the grade with respect to his/her percentage.

Final exam score calculator is mostly used in the educational institutions to predict the grading of their students & the grading system often requires the final percentage of score of the students. Final exam calculator helps tutors to calculate score which helps the institutions to know the ranking of their university according to their pass percentage of the students.

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standard deviation table

Let us learn about standard deviation table

Standard deviation table, a standard normal table also known as the "Unit Normal Table" is a math table for the values of Φ, the cumulative distribution function of the normal distribution. Standard deviation table are used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, & by extension, any normal distribution.

Standard deviation table is the measure of describing squared mean difference variability & spread of the Data set in the given total numbers. Standard deviation table is used to take the measurement of taking square root and average of numbers in the Data set.

Formula for standard deviation,

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logarithm solver

Let us solve problem using logarithm solver

Solve for x: 5^x = 2.

Apply the logarithm of both sides.

log 5^x = log 2

Use theorem 2 to simplify the equation.

x * log 2 = log 5

Solve for x by dividing each side by log three

x = (log 5/log 2)

A decimal approximation may be found if desired -

x = 2.32192809.

Solve Log₃(2x+5) = 2 for x.

Write an equivalent exponential expression, 2x+5= 3²

2x+5=3*3

2x+5=9

Solve for x. 2x=4, x = 2.

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equivalent fractions calculator

Let us solve problem using equivalent fractions calculator

Convert 9.6 to equivalent fraction number by using equivalent fractions calculator

Here transfer 9.6 to an equivalent fraction,

Multiply both the numerator & the denominator by 10.

= (9.6 x 10)/10

= 96/10

Hence there is one digit in a place of the very last digit is the "10th" decimal place. Therefore we can just say that 0.1 is the same as 1/10.

= 9.6 can be written as the equivalent fraction = 96/10

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maxima and minima

Let us learn about maxima and minima

A function is refers to be monotonic if it is either increasing or decreasing but not both in a given interval.

Consider the function f(x) = 3x+1, x£ [0,1]

The mentioned function is increasing function on R. Hence continuous function is a monotonic function in [0, 1]. Continuous function has its minimum value at x = 0 that is equal to f (0) =1, has a maximum value at x = 1, that is equal to f (1) = 4.

'Every monotonic function imagines its maximum or minimum values at the end points of its domain of definition.'

Point to be remember that 'every continuous function on a closed interval has a maximum and a minimum value

The maxima and minima value of an expression or quantity is meant primarily the "greatest" or "least" value which it can receive. However, there are notes at which its value ceases to increase & begins to decrease; its value at such a point is known a maximum. So there are points at that its value ceases to decrease & begins to increase; such a value is known as a minimum. There may be many maxima or minima, & a minimum is not necessarily less than a maximum. For illustration the expression (x 2 -1x+ 2)/(x - 1) can driven all values from - 00 to - 1 & from + 7 to + oo, but has, so long as x is real, no value between - 1 & + 7. Here - 1 is a maximum value, & + 7 is a minimum value of the expression, though it can be made greater or less than any assignable quantity.

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