Mathematics for Machine Technology
Mathematics for Machine Technology
7th Edition
ISBN: 9781133281450
Author: John C. Peterson, Robert D. Smith
Publisher: Cengage Learning
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Chapter 57, Problem 78A
To determine

The area of the metal plate.

Expert Solution & Answer
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Answer to Problem 78A

Area of stamping As =193.605.

Explanation of Solution

Concept used:

The metal sheet is divided into three trapeziums and a rectangle as shown.

  Mathematics for Machine Technology, Chapter 57, Problem 78A

The area of three trapeziums is added and the area of rectangle is subtracted from the metal plate to find the required area.

Calculation:

Area of whole rectangle A=l×w

Here, length l = 46 ft and Width w = 42 ft

By substituting the above values in the formula;

  A= 46 × 42A= 1932ft___________(1)

Area of trapezium (2), A2=12×h(b1+b2)

Here, height h = 6.50 ft, base b1= 9 ft and base b2= 14 ft

  A2=12×6.50(9+14)A2=12×6.50×23A2=74.75ft2_________(2)

Since the dimensions of trapezium (2) and (3) are same thus, from symmetry

The area of trapezium (3), A3=74.75ft2_________(3)

Again, Area of trapezium (4), A4=12×h(b1+b2)

Here, height h = 6.50 ft, base b1= 11 ft and base b2= 16 ft

  A4=12×6.50(11+16)A4=12×6.50×27A4=87.75ft2_________(4)

And,

The area of rectangle, Ar=l×w

Here, length l = 12.50 ft and

Width w = 42 − 28 = 14 ft

By substituting the above values in the formula;

  Ar= 12.50×14Ar= 175ft___________(5)

Now, Adding the equations (1), (2), (3) and (4) and subtract equation (5) to calculate the required area of metal plate.

Thus,

  A=A1+A2+A3+A4ArA=1932+74.75+74.75+87.75175A=1994.25ft

Conclusion:

Thus, the area of stamping is As =193.605.

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