Part 4

An alternative method of doing these examples is to proceed exactly as though you were multiplying all the factors together, except that whenever you come to a number in the denominator you use the CI scale instead of the C scale. The reader is advised to practice both methods and use whichever one he likes best.

3. The area of a circle. The area of a circle is found by multiplying 3.1416=PI by the square of the radius or by one-quarter the square of the diameter

Formula: A = PI * square( R ) A = PI * ( square( D ) / 4 )

Example 58: The radius of a circle is 0.25 inches; find its area.

Area = PI * square(0.25) = 0.196 square inches.

Set left-hand index of C scale over 0.25 on D scale. square(0.25) now appears above the left-hand index of the B scale. This can be multiplied by PI by moving the indicator to PI on the B scale and reading the answer .196 on the 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.