Chapter 6, Problem 13A

Refer to the shaft shown in Figure 6-4. Determine the missing dimensions in the table using the dimensions given. All dimensions are in inches.

To determine

(a)

Evaluate the missing dimension $B$ and $E$.

Answer to Problem 13A

The missing dimension $B$ and E are $4\frac{7}{8}\text{in}$ and $5\frac{1}{16}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown below:

  

  

Calculation:

Dimension $B$ is calculated as follows:

Subtract addition of $A$ and $C$ from $D$.

  $\begin{array}{l}B=D-(A+C)\\ B=6\frac{3}{4}-\left(\frac{1}{2}+1\frac{3}{8}\right)\\ B=\frac{54-15}{8}\\ B=\frac{39}{8}\\ B=4\frac{7}{8}\text{in}\end{array}$

Dimension $E$ is calculated as follows:

Subtract addition of $F$ and $C$ from $G$.

  $\begin{array}{l}E=G-(F+C)\\ E=7\frac{3}{8}-\left(\frac{15}{16}+1\frac{3}{8}\right)\\ E=\frac{118-37}{16}\\ E=\frac{81}{16}\\ E=5\frac{1}{16}\text{in}\end{array}$

Thus, the missing dimension $B$ and E are $4\frac{7}{8}\text{in}$ and $5\frac{1}{16}\text{in}$ respectively.

Conclusion:

The missing dimension $B$ and E are $4\frac{7}{8}\text{in}$ and $5\frac{1}{16}\text{in}$ respectively.

To determine

(b)

Evaluate the missing dimension $A$ and $G$.

Answer to Problem 13A

The missing dimension $A$ and G are $\frac{35}{64}\text{in}$ and $6\frac{3}{4}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown below:

  

  

Calculation:

Dimension is calculated as follows:

Subtract addition of $B$ and $C$ from D.

  $\begin{array}{l}A=D-(B+C)\\ A=5\frac{37}{64}-\left(3\frac{13}{32}+1\frac{5}{8}\right)\\ A=\frac{357-322}{64}\\ A=\frac{35}{64}\text{in}\end{array}$

Dimension G is calculated as follows:

Add of C, E and F.

  $\begin{array}{l}G=E+F+C\\ G=4\frac{3}{8}+\frac{3}{4}+1\frac{5}{8}\\ G=\frac{35+6+13}{8}\\ G=\frac{27}{4}\\ G=6\frac{3}{4}\text{in}\end{array}$

Thus, the missing dimension A and G are $\frac{35}{64}\text{in}$ and $6\frac{3}{4}\text{in}$ respectively.

Conclusion:

The missing dimension A and G are $\frac{35}{64}\text{in}$ and $6\frac{3}{4}\text{in}$ respectively.

To determine

(c)

Evaluate the missing dimension C and D.

Answer to Problem 13A

The missing dimension C and D are $1\frac{1}{16}\text{in}$ and $5\frac{19}{32}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown below:

  

  

Calculation:

Dimension C is calculated as follows:

Subtract addition of E and F from G.

  $\begin{array}{l}C=G-(E+F)\\ C=7\frac{1}{32}-(5\frac{1}{8}+\frac{27}{32})\\ C=\frac{225-191}{32}\\ C=\frac{34}{32}\\ C=1\frac{1}{16}\text{in}\end{array}$

Dimension D is calculated as follows:

Add of A, B and C.

  $\begin{array}{l}D=A+B+C\\ D=\frac{7}{16}+4\frac{3}{32}+\frac{34}{32}\\ D=\frac{14+131+34}{32}\\ D=5\frac{19}{32}\text{in}\end{array}$

Thus, the missing dimension C and D are $1\frac{1}{16}\text{in}$ and $5\frac{19}{32}\text{in}$ respectively.

Conclusion:

The missing dimension C and D are $1\frac{1}{16}\text{in}$ and $5\frac{19}{32}\text{in}$ respectively.

To determine

(d)

Evaluate the missing dimension B and E.

Answer to Problem 13A

The missing dimension B and E are $3\frac{29}{32}\text{in}$ and $5\frac{5}{8}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown below:

  

  

Calculation:

Dimension B is calculated as follows:

Subtract addition of A and C from D.

  $\begin{array}{l}B=D-(A+C)\\ B=5\frac{31}{32}-(\frac{5}{8}+1\frac{7}{16})\\ B=\frac{191-66}{32}\\ B=3\frac{29}{32}\text{in}\end{array}$

Dimension E is calculated as follows:

Subtract addition of C and F from G.

  $\begin{array}{l}E=G-(C+F)\\ E=7\frac{15}{16}-(1\frac{7}{16}+\frac{7}{8})\\ E=\frac{127-37}{16}\\ E=\frac{45}{8}\\ E=5\frac{5}{8}\text{in}\end{array}$

Thus, the missing dimension B and E are $3\frac{29}{32}\text{in}$ and $5\frac{5}{8}\text{in}$ respectively.

Conclusion:

The missing dimension B and E are $3\frac{29}{32}\text{in}$ and $5\frac{5}{8}\text{in}$ respectively.

To determine

(e)

Evaluate the missing dimension A and G.

Answer to Problem 13A

The missing dimension A and G are $\frac{19}{32}\text{in}$ and $7\frac{27}{64}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown below:

  

  

Calculation:

Dimension A is calculated as follows:

Subtract addition of B and C from D.

  $\begin{array}{l}A=D-(B+C)\\ A=6\frac{1}{32}-(3\frac{3}{4}+1\frac{11}{16})\\ A=\frac{193-174}{32}\\ A=\frac{19}{32}\text{in}\end{array}$

Dimension G is calculated as follows:

Add C, E and F.

  $\begin{array}{l}G=C+E+F\\ G=1\frac{11}{16}+4\frac{61}{64}+\frac{25}{32}\\ G=\frac{108+317+50}{64}\\ G=\frac{475}{64}\\ G=7\frac{27}{64}\text{in}\end{array}$

Thus, the missing dimension A and G are $\frac{19}{32}\text{in}$ and $7\frac{27}{64}\text{in}$ respectively.

Conclusion:

The missing dimension A and G are $\frac{19}{32}\text{in}$ and $7\frac{27}{64}\text{in}$ respectively.

To determine

(f)

Evaluate the missing dimension C and D.

Answer to Problem 13A

The missing dimension C and D are $\frac{63}{64}\text{in}$ and $5\frac{55}{64}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown below:

  

  

Calculation:

Dimension C is calculated as follows:

Subtract addition of E and F from G.

  $\begin{array}{l}C=G-(E+F)\\ C=7\frac{3}{64}-(5\frac{3}{16}+\frac{7}{8})\\ C=\frac{451-388}{64}\\ C=\frac{63}{64}\text{in}\end{array}$

Dimension D is calculated as follows:

Add of A, B and C.

  $\begin{array}{l}D=A+B+C\\ D=\frac{11}{16}+4\frac{3}{16}+\frac{63}{64}\\ D=\frac{44+268+63}{64}\\ D=5\frac{55}{64}\text{in}\end{array}$

Thus, the missing dimension C and D are $\frac{63}{64}\text{in}$ and $5\frac{55}{64}\text{in}$ respectively.

Conclusion:

The missing dimension C and D are $\frac{63}{64}\text{in}$ and $5\frac{55}{64}\text{in}$ respectively.