The diameter of the injection cylinder is 8 inches, and the diameter of the screw is 2.5 inches. What is the Intensification Ratio? (Round to the second decimal point)
Understand the Problem
The question asks us to calculate the Intensification Ratio given the diameters of the injection cylinder and the screw. The Intensification Ratio is often calculated as the square of the ratio of the cylinder diameter to the screw diameter. We need to calculate that and round that result to the second decimal point.
Answer
10.24
Answer for screen readers
10.24
Steps to Solve
- Calculate the ratio of the cylinder diameter to the screw diameter.
Divide the diameter of the injection cylinder by the diameter of the screw. $$ \frac{8}{2.5} $$
- Square the ratio.
Square the result from the previous step to find the intensification ratio. $$ (\frac{8}{2.5})^2 $$
- Simplify the expression.
$$ (\frac{8}{2.5})^2 = (3.2)^2 = 10.24 $$
- Round to the second decimal point.
The result is already at the second decimal point (10.24) so no further rounding is needed.
10.24
More Information
The intensification ratio is a dimensionless number.
Tips
A common mistake might be forgetting to square the ratio. Another could be incorrectly dividing the diameters (i.e., dividing the screw diameter by the cylinder diameter). Also, not rounding to the correct number of decimal places would result in a wrong answer.
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