The coefficient of thermal expansion for volume is usually 3 times the coeficcient for expansion for length
To estimate the cube for a number between 1 and 1.1
Step 1
Subtract 1 from the number
Step 2
Multiply the quantity you calculated in step 1 by 3
Step 3
Add 1 to the number you calculated in step 2
Finished
Only for numbers in the range that happens to be used for thermal expansion calculations for some materials near room temperature when the temperature change is small enough
I do not think it works for large numbers
The sine of theta in radians is also close to theta for angles smaller than a certain angle but not for angles larger than a certain angle
The volume is not three times the length
the change in volume is approximately three times the change in length
If the change in length is less than 10% the original length
If the increase in length is less than 10% and greater than 0% it approximately works
It should not work for a decrease in length
I would not know how to use the method to calculate cubes for numbers above 4/3 because 3*4/3=2
And I am looking at the digits after 1 when you cube a number above 1 written as a decimal
1.3333333333333333^3
is approxinstely equal to
1.9999999999999999^3
according to the drecribed estimation technique
(4/3)^3 is approximately equal to 2
3"((4/3)-1)+1 = 2
You are multiplying the digits after 1 by 3 and keeping the ones digit the same for numbers greater than or equal to 1 and less than or equal to 4/3
1 of 2
You can do the same thing for bigger numbers by sutracting 1 then mu!tiplying the number by 3 then adding 1 in that order
(1.75-1)*3+1 =3.25
1.75^3=5.359 rounded
2 of 2
