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Understanding Metric Conversions and Cost Calculations in Engineering

This document provides detailed solutions for various engineering mathematics problems, including metric conversions and cost calculations. It covers the transformation of metres to millimetres, the impact of decimal rounding, and understanding scale on technical drawings. Additionally, it explains volume calculations for liquids, tank dimensions, and associated costs of materials based on specific measurements. Key principles in measurement, rounding techniques, and area calculations are discussed, helping learners grasp essential mathematical applications in engineering contexts.

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Understanding Metric Conversions and Cost Calculations in Engineering

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  1. MathsAnswersM&E

  2. Question 1 • Metres into millimetres. • 1000mm in 1 metre • 0.5842 is around half a metre (500mm). • Therefore 0.562 is 562mm

  3. Question 2 • Shaft diameter is to be machined to 60.56mm • Maximum allowable diameter is • 60.56 + 0.02mm • = 60.58 mm

  4. Question 3 • Scale of 1:20 mean for every 1 mm on the drawing represents 20 mm in real life. • Therefore if the actual length is 120mm then • The drawing size is 120/20 • = 6mm

  5. Question 4 • To round off if the decimal place number is a 5 or more then the number to the left of the point goes up one digit. If it is 4 or less then the number stays the same. • Rounding of to one decimal place • 23.25 = • 23.3 (as the 5 makes the 2 rounded up) • 23.24 = • 23.2 (4 makes the 2 stay the same)

  6. Liquids and volume • 1000 mm or 1 metre square holds • 1000 litres • 1 cm2 = 1mL • 1000mL = 1 Litre • 100cm x 100cm x 100cm = 1000000 cm2 • Divide by 1000 = 1000 litres • A carton of milk holds 1 litre as its dimensions are approx 200 x 70 x 70mm = 20cm x 7cm x 7cm = 980 cm2 or 980/1000 = 0.98 Litres

  7. Question 5 • Tank is 1.2 x 1 x 2 = total of 2.4m2 or • 2400 litres

  8. Question 6 • Total length of weld = 2 sides of 975 • 2 ends of 835 • 4 vertical welds of 685 • = 2 x 975 + 2 x 835 + 4 x 685 = • 6360

  9. Question 7 • Cost of the frame for the tank= • 2 x 975 + 2 x 835 + 4 x 50 • =3820 mm or 3.820 metres • Cost per metre is $ 2.00 • Total cost is 3.820 x $2.00 • = $7.64

  10. Sheet measurements • Use the length of the sheet for the circumference measurement (the longer measurement).

  11. The height of the bin is set at 350 350

  12. Question 8 • Diameter of the bin is 400 mm • Height of the bin is 350mm • Base = 400 +10+10 • To find the circumference then use • 400 x pi = 1257mm

  13. Sheet measurements • 1257mm. 1200 2400

  14. Sheet measurements • 1257mm+ 40mm fold = 1297mm.

  15. Sheet measurements • 1257mm+ 40mm fold = 1297mm • + bin base = 400 + 20 (fold)= 1717mm.

  16. Sheet measurements 420 • 1257mm+ 40mm fold = 1297mm+ bin base = 400 + 20 (fold)= 1717mm. • Cut along black lines 1717 x 420 350 1717 350 420

  17. Sheet measurements 420 • Area of sheet 2.400 x 1.200 = 2.88m2 • Area of section 1.717 x 0.350= 0.600m2 350 1717 350 420

  18. Sheet measurements 420 • 2.88m2 = $45.00 cost per m2 = 45/2.88 = $15.625 • Area of section 1.717 x 0.350= 0.600m2x $15.625 = $9.37 • Or 0.6/2.88 x $45.00 = $9.37 350 1717 350 420

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