What is the average length, in inches, of the pieces? Six welding jobs are completed using 33 pounds, 19 pounds, 48 pounds, 14 pounds, 31 pounds, and 95 pounds of electrodes. What is the average poundage of electrodes used for each job?
On 5 jobs, a welder charges 6. Find the average hours billed per job. Four pieces of steel plate are measured for thickness. These measurements are found: 1 1s 3 s 1s 1s ,1 ,1 ,1 4 16 4 2 What is the average thickness of the plate?
Round the answer to the nearest thousandth. Find the average weight of the plates to the nearest thousandth pound. Six plates are stacked and weighed. The total weight is pounds. What is the average weight of each piece?
A welded steel tank holds gallons. Another tank holds twice as much. What is the average amount held by the tanks? Example 1: A customer places an order with your company for 40 welded brackets. Formulate a fraction from the information given. Change the fraction into a decimal. Procedure: a. Answer: B. In this case, the fraction reduced to the whole number 1. The decimal now needs to be shown.
S Example 2: Step 1 S S. Example 1: Answer: Change Multiply the given number by that decimal. However, there is a 7. How much will you save with the 7. What is 7. Step 1 Change 7. What is the price of the cutting outfit after the discount? What is your final cost?
Express each percent as a decimal. Calculate: a. Social Security c. The area of a piece of steel is How many completed welds are made? A total of 80 coupons weld test plates are submitted for certification and all are inspected. Use the information given to calculate a. In a mill, 10, steel plates are sheared. How many plates are rejected? How many of the rejected plates are scrapped? Fraction Example: 1 4 Decimal. It is used in an effort to attract business and compete with other suppliers.
It is similar to percentages in that a. Note: Other factors can affect the decision-making process when selecting a supplier.
Huff Steel offers a. TD Mfg. Which company offers lower landed material costs, and what is that cost? Steel USA uses a multiplier of. They also include an additional net offer on the bill. Prior to metrics, English measure consisted of a multitude of measurements, some of with which we are familiar; others have meanings that are antiquated.
Examples: inch foot yard mile hand ell furlong pole or perch fathom league Although the United States still uses a mixture of English and metrics, most other countries in the world use only the metric system. The meter is the standard unit of measurement of length in the metric system. Example: A measurement of two and one-half millimeters is written: 2. What is the length in millimeters? See the metric length measure table. Since the measurement is in centimeters, each 1 cm contains 10 millimeters.
Example: cm The illustrated rod is cm long. What is the length in meters? Solution: Divide by Since the measurement is in centimeters, each group of cm equals 1 meter.
Read the distances, in millimeters and then in centimeters, from the start of the rule to the letters A—H on the rule. This piece of steel channel has a length of 22 millimeters. Express this measurement in centimeters. How many centimeters are there in 1 meter?
A pipe with end plates is shown. Find the length of the pipe section in the weldment in millimeters. Find the thickness of one end plate in millimeters. Find the overall length in meters. This piece of bar stock is cut into pieces, each 7 centimeters long. How many pieces are cut? Disregard cutting waste a. A shaft support is shown. Find the overall height of the shaft support in centimeters. Express the length of the steel plate in millimeters.
Express the width of the steel plate in centimeters. This shaft is turned on a lathe from a piece of cold-rolled round stock.
Find the total length in centimeters. Find the total length in meters. Nine pieces of this pipe are welded together to form a continuous length. What is the length, in meters, of the welded section? English-Metric Equivalents 1 inch in 5 Reminder: Round off the answer only after calculations are made. The round stock is Express this length in meters. Round the answer to the nearest thousandth meter. Find the diameter of the round stock to the nearest hundredth millimeter.
This I beam is cm long and Round each answer to two decimal places. Express the length in inches. Express the height in inches. A piece of plate stock is shown. Express the plate thickness in centimeters. Express the plate width in centimeters and meters. Express the plate length in centimeters and meters. Express in meters the length and width of the following object. Express the height in millimeters. Note: Convert fractions to decimals to solve Problems 5 and 6.
Express each measurement in millimeters. Review the tables of equivalent units in Section 2 of the Appendix. This drawing shows a welded pipe support. Express the height in meters. Express the width in meters, centimeters, and feet.
This steel gusset is a right angle triangle. Express side A in centimeters. Express side B in centimeters and millimeters. A pipe bracket is shown. Round all answers to three decimal places. Find the width of the pipe bracket dimension A in millimeters. What is the length of the pipe bracket dimension B in millimeters?
Find the distance between the center of the holes dimension C in centimeters. Note: Use this diagram for Problem 7. PART B A welder makes 20 of these table frames. How many centimeters of square steel tubing are required to complete the order for Part A? How many centimeters of square steel tubing are required to complete the order for Part B? How many meters of square steel tubing are required to complete the order for Part C? Square: A four-sided figure, as shown below.
All four sides are of equal length, and all four angles are The lengths are equal only to each other and the widths are equal only to each other.
All four angles are Note: Length is designated on drawings with the letters L, l, or ,. Examples: a. A formula is a set of math instructions that solve a specific problem. Example 1: What is the perimeter of square A? All four sides are 80 in length.
Step 2 Calculate multiplication and division. For clarity, parentheses can be placed around these operations. Step 3 Calculate addition and subtraction. Example: Solve the following: This problem includes parentheses given. Step 2 illustrates parentheses added for clarifying the order of operations. Step 3 Answer: 32 1 8 3 5 2 3 2 4 4 2 5 5 23 5 23 Practical Problems 1. The measure of one side of square plates is given. Calculate the perimeter of each plate.
Find the perimeter of the following rectangles: a. Area: Two dimensional space—length and width The following illustrates the development of 1 square foot into square inches. However, in this case, the exponent is used to show that the object in the answer, square centimeters, has a.
Study the work in the solution again. Notice that the exponent has two different uses: Its first use is as a math instruction. Example: How many square inches are in a rectangular plate measuring 80 3 30? Find the area of each square. Square A 2. Square B 3. Square C 4. How many square inches are in 1 square foot? The four pieces of sheet metal are cut for a welding job. Find the area of rectangle A in square inches. Find the area of rectangle B in square inches.
Find the area of rectangle C in square inches. Find the area of rectangle D in square inches. What is the total area of the pieces in square inches? Express the total area in square feet. Which of the pieces has an area of 1 square foot? A rectangular tank is made from plates with the dimensions shown. Find the total area of plate needed to complete the tank in square inches. How many square feet of plate is needed? It is a three-sided figure containing three angles totaling The width of the rectangle is the same label as the height of the triangle.
These four triangular shapes are cut from sheet metal. What is the area of each piece in square inches? Triangle A 2. Triangle C 4. Triangle D Note: Use this information for Problems 5 and 6.
Two pieces of sheet metal are cut into triangular shapes. Find, in square centimeters, the area of triangle A. Find, in square inches, the area of triangle B. Trapezoids Definition A trapezoid is a four-sided figure in which only two of the sides are parallel.
Labeling A trapezoid uses the same labeling as a triangle for measurements: base s and height. The trapezoid has two bases lengths , so we need to find the average base. Step 1 B1b 5 average base 2 Step 2 Multiply average base times the height. Gusset A 8. Gusset B 9.
Gusset C Gusset D One-hundred-twenty support gussets are cut as shown. Find, in square feet, the total area of steel plate needed for the complete order. A welded steel bin is made from plates with these dimensions. Find, in square centimeters, the amount of plate used to complete the bin. The amount of space occupied in a three-dimensional figure is called the volume. Volume is also the number of cubic units equal in measure to the space in that figure.
The formula for the volume of a cube is: Volume 5 side 3 side 3 side or V 5 s3 The exponent 3 describes the math procedure. It contains 8 cubic inches of space or material. The exponent in the answer 3 shows that the object, cubic inches, is three-dimensional: it has length, width, and height or depth. Volume: three-dimensional space with length, width, and height.
Answer: Total cubic inches in 1 cubic foot ft3 5 in3 Practical Problems 1. A solid cube of steel is cut to these dimensions. Find the volume of the cube in cubic inches. Find the volume in cubic feet. Five pieces of 5. Find the total volume of the pieces in cubic centimeters. Two pieces of square stock are welded together.
Find, in cubic feet, the total volume of the pieces. Round the answer to three decimal places. Sheet metal is bent to form this cube. What is the volume of the completed cube in cubic inches? Find, in cubic inches, the volume of each steel bar. Steel bar A 6. Steel bar B 7. Steel bar C Find the volume of each rectangular solid. If outside measurements are given, the wall thicknesses are subtracted as a first step. How many gallons will the tank hold? Note: There are in3 in one gallon.
Solution: Divide into the volume found. These are inside dimensions. Round each answer to three decimal places. The dimensions on this box are inside dimensions.
Find the number of cubic inches of volume in the box. Note: There are 1, cm3 cubic centimeters in one liter. To find the number of liters a tank or container can hold, divide the volume cm3 by 1, Example: A tank measuring 50 cm by 32 cm by 32 cm is built. Determine the volume in cubic centimeters, and find the number of liters the tank can hold.
Solution: Step 1 V 5 , wh 5 50 cm 3 32 cm 3 32 cm 5 51, cm3 Step 2 51, 5 The dimensions on this welded square box are inside dimensions. Find the number of liters that the tank can hold.
Round the answer to tenths. Outside measurements are given. Find the volume of tank A. Round the answer to the nearest tenth cubic inch. Find the volume of tank B. The dimensions of welded storage tanks C and D are inside dimensions. The dimensions of tank D are exactly twice those of tank C. Is the volume of tank D twice the capacity of tank C? Cubed tanks A, B, C, and D are welded and filled with a liquid. Which of the tanks has a volume closest to one gallon?
The dimensions are inside dimensions. Nine fuel storage tanks for pickup trucks are welded. What is the total volume, in cubic inches, of the entire order of tanks? What is the total volume in cubic feet? How many gallons does the tank hold? This welded tank has two inside dimensions given.
The tank holds Find, to the nearest tenth inch, dimension x. This rectangular welded tank is increased in length, so that the volume, in gallons, is doubled. What is the new length dimension x after the welding is completed? A pickup truck tank holds 89 liters of gasoline. Two auxiliary tanks are constructed to fit into spaces under the fenders of the truck.
What is the total volume of the two tanks plus the original tank? This welded steel tank is damaged. The section indicated is removed and a new bulkhead welded in its place. How many fewer liters will the tank hold after the repair? Circle: A circle is a closed curved object, all parts of which are equally distant from the center.
Symbol used is C. Radius: The radius is a straight line measurement from the center to the edge of the circle; it is one-half the diameter.
Symbol used is r. It divides the circle in half, and is equal in length to 2 radii. Symbol used is D. The number 3. Welding shops round p to 3. The formula for calculating the circumference of a circle is C 5 pD Example: Using chalk and a rule, a circle with a diameter of is marked on steel plate. How many inches does the chalk travel in drawing a complete circle? Solution: C 5 pD 5 3. What is the circumference of both circles in inches? In feet? What is the circumference of a circle that has a radius of 6.
The Earth has an average diameter of approximately 7, miles. What is its average circumference? Example: What is the distance around this semicircular figure? The perimeter of a semicircular-sided form is a. A semicircular-sided tank is welded in a shop. How long is the piece of metal used to form the sides of the tank? Find the distance around this semicircular-sided tank.
A steel tank is welded as shown. Find, in square inches, the area of the circular steel bottom. What is the area of a circle that has a diameter of 29 cm? Express the answer in cm2, in2, ft2, m2. A 5 ,w 5 3 59 5 50 ft2 Step 3 Answer: Express each answer in square inches. WASTE 41" 37" 79" " a. Find the area of the original plate. Find the area of the semicircular-sided tank bottom.
Find the waste from the original plate. Find the area of each semicircular-sided tank bottom. Express each area in square inches. Bottom A 5. Bottom B 6. When this is multiplied by the height of the cylinder, the volume is found. Example: What is the volume of a cylinder with a radius of 60 and a height of 90? Find, in cubic inches, the volume of 17 of these small welded hydraulic tanks.
Inside dimensions are given. Semicircular-Shaped Tanks and Solids RULE: The volume of this semicircular-shaped solid is equal to the sum of the two semicylinders at the ends, and the rectangularly-shaped piece in the center. Dimensions given are inside dimensions. Reminder: All dimensions must be in the same unit of measure before calculating: inches and inches, feet and feet, and so on. What is the volume of this semicircular-sided solid in cubic feet? Two semicircular-sided tanks are shown.
The dimensions of one tank are exactly twice the dimensions of the other tank. Is the volume of the larger tank twice the volume of the smaller tank?
Explain volume comparison B. If outside dimensions are given, subtract wall thicknesses as a first step. Review volume formulas from previous chapters. A pipe with an outside diameter of 10 inches is cut into 3 pieces. Find the volume of each piece, in cubic inches.
Pipe wall thickness is. C 7'-9" B A 6'-3" 6'-8" a. Piece A a. Piece B b. Piece C c. An outside storage tank is welded.
The dimensions given are inside dimensions. Find, in cubic meters, the volume of the tank. Find, in liters, the volume of the tank. The dimensions on these three cylindrical welded tanks and connecting pipes are inside dimensions. The tanks are connected as shown and are filled with liquid.
The system is completely filled, including the connecting pipes. What is the total volume of the system? A two-piece elbow is cut and welded from a Find the volume of the elbow to the nearest hundredth cubic meter.
Two settling tanks are welded together. Find, in gallons, the volume of the entire system. Round the answer to the nearest tenth gallon. A length of welded irrigation pipe has the dimensions shown. Twenty of these lengths are welded together. What is the total volume of the welded pipes?
A weldment consisting of a semicircular-sided tank and a steel angle frame is constructed as shown. What is the volume of the complete tank to the nearest gallon? Using semicircular-sided pipes, this manifold system is welded. Find, in cubic inches, the total volume of the pipes. Find, in cubic inches, the volume of the tank. Find, in gallons, the volume of the entire manifold system. Example 1: A 90 piece of steel round stock has a diameter of Calculate the weight.
Fourteen pieces of cold-rolled steel shafting are cut as shown. What is the total weight of the 14 pieces of steel in pounds? Steel angle legs for a tank stand have the dimensions shown. Find the weight of 20 legs in kilograms.
A circular tank bottom is cut as shown. Find the weight of the circular bottom. Find the weight of the wasted material. What is the total weight, in pounds, of the 5 pieces used for the bin? Sixteen circular blanks for sprockets are cut from 1. What is the weight of 1 blank in kilograms?
What is the weight of all of the blanks in kilograms? Find, in pounds, the weight of 1 piece of the bar stock. Skip to content My Bookshelf. The topics are presented in a step-by-step approach.
Clear examples facilitate learning and improve understanding of the basics. Students have different math education backgrounds and may have learned their math skills through different approaches.
This text teaches traditional basic math in a concise and straightforward way. Save money and simplify with Cengage Unlimited.
Show your students how welders rely on mathematical skills to solve both everyday and more challenging problems, from measuring materials for cutting and assembling to effectively and economically ordering materials.
Highly readable, inviting units throughout this comprehensive, new edition emphasize the types of math problems welders regularly face, from basic math procedures used in standard operations to more advanced formulas. This edition reflects the latest developments in the welding industry using a wealth of real examples; new practice problems; and clear, uncomplicated explanations.
The book's carefully constructed approach is ideal for students of all levels of math proficiency and experience. New, more dimensional illustrations throughout this edition help students further visualize the concepts they're learning.
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