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
I would say that for small angles in radians the sine of theta being approximately equal to theta is because of a relationship
When an angle is small enough
Where the angle measures both a section of a circle and also is an angle within a triangle
When the largest side of a triangle is the same as the radius of the circle
the perimeter of a section of a circle having an angle of theta
is close to the length of a side in a right angle triangle having an angle of theta
Do you know what the sine function actually does?
Small angle approximation formulas for trigononetry
If you have a ramp on the ground at an angle measured relative to the ground where the angle is zero if the ramp is parellel to the ground
The tangent converts the angle to a slope
The sign gives you the height of the ramp divided by it's diagnol path
The cosine gives you the horizontal distance divided by it's diagnol path
You can also do ratios of side lengths given dimensions of triangles using the names opposite, adjacent and hypoteneous but this is harder to visualize
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
Volume and length are actually related.