Linear Equations and Inequalities

A . Measurement of Volume of a Rectangular Solid

Theory

A rectangular solid is the one all the faces of which are rectangular It has six rectangular faces . Volume (V ) of a Rectangular Solid is given by following equation

V l b h (1

Where `l ' is length , `b ' is breadth and `h ' is height of the rectangular solid

Procedure

A rectangular wooden block was identified in my house . It happened to be a designer piece of glass gifted by someone to my father and it was used as weight

on his table

A plastic scale of 15 cm length was chosen to measure the dimensions of this glass piece

This scale has markings to one tenth of a cm

The scale was put on the glass block such that one of the marking say 2cm marking is perfectly aligned with one of the edges of the rectangular solid . Reading of the scale at the other edge was taken upto one tenth of a cm

Reading on the left was subtracted from that on the right side and this gives the length of one of the edges of the rectangular solid

The same was repeated to get length of the remaining two edges of the solid

The values were recorded in a note-book

Data and Calculation

Following values were obtained for the length (l , breadth (b ) and height (h ) of the rectangular solid

Length l 5 .6 cm Breadth b 3 .6 cm Height h 2 .6 cm

Using the formula in equation 1

Volume of the rectangular solid V l b h 5 .6 cm 3 .6 cm 2 .6 cm 52 .4 cm3

Conclusion

Volume of a rectangular object was calculated using the measured values of its length , breadth and height . The calculated volume of the rectangular object is 52 .4 cm3

A . Real Life Application of a Linear Function

Suppose we put a sum of money say

in a bank account that gives simple interest at the rate r per year , irrespective of the period for which the money remains invested in the bank . Then , the future value (A ) of the invested sum

, after t years will be given by following linear function

A

P r t

Suppose I invest 1000 in such an account which gives me 6 per year and there is no compounding at all . The after t years value of my investment will be given by

A 1000 1000 0 .06 t

Let us take t 2 , it means I am talking about a time two years from now then value of A will be

A 1000 1000 0 .06 2 1000 120 1120

This means two years from now , if I choose to withdraw my fund from the bank I will get 1120

Let us take t 5 , it means I am talking about a time five years from now then value of A will be

A 1000 1000 0 .06 5 1000 300 1300

This means two years from now , if I choose to withdraw my fund from the bank I will get 1300 ...