Question

# Determine the overall length, width, and height of the casting in Figure 2-4. All dimensions are in inches.

Solution

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Step 1
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To find the overall length, add the horizontal dimensions:

$l=\dfrac{17}{32}+\dfrac{63}{64}+\dfrac{3}{8}$

Write using the CLD which is 64:

$l=\dfrac{17}{32}\cdot \dfrac{2}{2}+\dfrac{63}{64}+\dfrac{3}{8}\cdot \dfrac{8}{8}$

$l=\dfrac{34}{64}+\dfrac{63}{64}+\dfrac{24}{64}$

$l=\dfrac{121}{64}$

$\color{#c34632}l=1\dfrac{57}{64}\text{ inches}$

To find the overall widtth, add the slanted dimensions:

$w=\dfrac{1}{4}+\dfrac{7}{16}+\dfrac{21}{32}$

Write using the CLD which is 32:

$w=\dfrac{1}{4}\cdot \dfrac{8}{8}+\dfrac{7}{16}\cdot \dfrac{2}{2}+\dfrac{21}{32}$

$w=\dfrac{8}{32}+\dfrac{14}{32}+\dfrac{21}{32}$

$w=\dfrac{43}{32}$

$\color{#c34632}w=1\dfrac{11}{32}\text{ inches}$

To find the overall height, add the vertical dimensions:

$h=\dfrac{29}{64}+\dfrac{9}{16}+\dfrac{5}{32}+\dfrac{1}{2}$

Write using the CLD which is 64:

$h=\dfrac{29}{64}+\dfrac{9}{16}\cdot \dfrac{4}{4}+\dfrac{5}{32}\cdot \dfrac{2}{2}+\dfrac{1}{2}\cdot \dfrac{32}{32}$

$h=\dfrac{29}{64}+\dfrac{36}{64}+\dfrac{10}{64}+\dfrac{32}{64}$

$h=\dfrac{107}{64}$

$\color{#c34632}h=1\dfrac{43}{64}\text{ inches}\color{white}\tag{1}$

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