Instruction for Using a Slide Rule | Page 6

A scale. This is an example where it is convenient to multiply with the A and B scales.
Example 59: The diameter of a circle is 8.1 feet. What is its area?
Area = (PI / 4) * square(8.1) = .7854 * square(8.1) = 51.7 sq. inches.
Set right-hand index of the C scale over 8.1 on the D scale. Move the indicator till hair-line is over .7854 (the special long mark near 8) at the right hand of the B scale. Read the answer under the hair-line on the A scale. Another way of finding the area of a circle is to set 7854 on the B scale to one of the indices of the A scale, and read the area from the B scale directly above the given diameter on the D scale.
4. The circumference of a circle. Set the index of the B scale to the diameter and read the answer on the A scale opposite PI on the B scale
Formula: C = PI * D C = 2 * PI * R
Example 60: The diameter of a circle is 1.54 inches, what is its circumference?
Set the left-hand index of the B scale to 1.54 on the A scale. Read the circumference 4.85 inches above PI on the B scale.
EXAMPLES FOR PRACTICE
61: What is the area of a circle 32-1/2 inches in diameter? Answer 830 sq. inches
62: What is the area of a circle 24 inches in diameter? Answer 452 sq. inches
63: What is the circumference of a circle whose diameter is 95 feet? Answer 298 ft.
64: What is the circumference of a circle whose diameter is 3.65 inches? Answer 11.5 inches
5. Ratio and Proportion.
Example 65: 3 : 7 : : 4 : X or (3/7) = (4/x) Find X
Set 3 on C scale over 7 on D scale. Read X on D scale under 4 on C scale. In fact, any number on the C scale is to the number directly under it on the D scale as 3 is to 7.
PRACTICAL PROBLEMS SOLVED BY SLIDE RULE
1. Discount. A firm buys a typewriter with a list price of $150, subject to a discount of 20% and 10%. How much does it pay?
A discount of 20% means 0.8 of the list price, and 10% more means 0.8 X 0.9 X 150 = 108.
To do this on the slide rule, put the index of the C scale opposite 8 on the D scale and move the indicator to 9 on the C scale. Then move the slider till the right-hand index of the C scale is under the hairline. Now, move the indicator to 150 on the C scale and read the answer $108 on the D scale. Notice that in this, as in many practical problems, there is no question about where the decimal point should go.
2. Sales Tax.
A man buys an article worth $12 and he must pay a sales tax of 1.5%. How much does he pay? A tax of 1.5% means he must pay 1.015 * 12.00.
Set index of C scale at 1.015 on D scale. Move indicator to 12 on C scale and read the answer $12.18 on the D scale.
A longer but more accurate way is to multiply 12 * .015 and add the result to $12.
3. Unit Price.
A motorist buys 17 gallons of gas at 19.5 cents per gallon. How much does he pay?
Set index of C scale at 17 on D scale and move indicator to 19.5 on C scale and read the answer $3.32 on the D scale.
4. Gasoline Mileage.
An automobile goes 175 miles on 12 gallons of gas. What is the average gasoline consumption?
Set indicator over 175 on D scale and move slider till 12 is under hair-line. Read the answer 14.6 miles per gallon on the D scale under the left-hand index of the C scale.
5. Average Speed.
A motorist makes a trip of 256 miles in 7.5 hours. What is his average speed?
Set indicator over 256 on D scale. Move slider till 7.5 on the C scale is under the hair-line. Read the answer 34.2 miles per hour under the right-hand index of the C scale.
6. Decimal Parts of an Inch.
What is 5/16 of an inch expressed as decimal fraction?
Set 16 on C scale over 5 on D scale and read the result .3125 inches on the D scale under the left-hand index of the C scale.
7. Physics.
A certain quantity of gas occupies 1200 cubic centimeters at a temperature of 15 degrees C and 740 millimeters pressure. What volume does it occupy at 0 degrees C and 760 millimeters pressure?
Volume = 1200 X (740/760) * (273/288) = 1100 cubic cm.
Set 760 on C scale over 12 on D scale. Move indicator to 740 on C scale. Move slider till 288 on C scale is under hair-line. Move indicator to 273