Chapter 2, Problem 15A

To determine

Evaluate the length of A, B, C, D, E and F of the part.

Answer to Problem 15A

The length of A, B, C, D, E and F of the part are $1\frac{1}{16}\text{in}$, $\frac{59}{64}\text{in}$, $1\frac{9}{16}\text{in}$, $\frac{11}{16}\text{in}$, $3\frac{11}{64}\text{in}$ and $\frac{13}{16}\text{in}$ respectively.

Explanation of Solution

Given:

All the dimensions are shown in below Fig:

Concept used:

Mark all the corner points as k, l, m, n, o, p, q, r, s, t, u, v, w, x, y and z.

  $\text{A}=pq+rs$   .... (1)

Here, distance A is the sum of distance $pq$ and $rs$ as marked in above Fig.

  $B=qr+st$   .... (2)

Here, distance B is the sum of distance $qr$ and $st$ as marked in above Fig.

  $\text{C}=uv+wx+yz$    .... (3)

Here, distance C is the sum of distance $uv$, $wx$ and $yz$ as marked in above Fig.

  $\text{D}=kl+mn$   .... (4)

Here, distance D is the sum of distance $kl$ and $mn$ as marked in above Fig.

  $\text{E}=\text{B+C+D}$...... (5)

Here, distance E is the sum of distance $\text{B}$, $\text{C}$ and $\text{D}$ as marked in above Fig.

  $\text{F}=zk+ml+no$    .... (6)

Here, distance F is the sum of distance $zk$, $ml$ and $no$ as marked in above Fig.

Calculation:

Substitute $\frac{1}{2}\text{in}$ for $pq$ and $\frac{9}{16}\text{in}$ for $rs$ in equation (1).

  $\begin{array}{c}\text{A=}\frac{1}{2}+\frac{9}{16}\\ \text{A}=\frac{17}{16}\\ \text{A}=1\frac{1}{16}\text{in}\end{array}$

Substitute $\frac{3}{8}\text{in}$ for $qr$ and $\frac{35}{64}\text{in}$ for $st$ in equation (2).

  $\begin{array}{c}\text{B=}\frac{3}{8}+\frac{35}{64}\\ \text{B}=\frac{24+35}{64}\\ \text{B}=\frac{59}{64}\text{in}\end{array}$

Substitute $\frac{31}{32}\text{in}$ for $uv$, $\frac{1}{8}\text{in}$ for $wx$ and $\frac{15}{32}\text{in}$ for $yz$ in equation (3).

  $\begin{array}{c}\text{C=}\frac{31}{32}+\frac{1}{8}+\frac{15}{32}\\ \text{C}=\frac{31+4+15}{32}\\ \text{C}=\frac{25}{16}\text{in}\\ \text{C}=1\frac{9}{16}\text{in}\end{array}$

Substitute $\frac{1}{4}\text{in}$ for $kl$ and $\frac{7}{16}\text{in}$ for $mn$ in equation (4).

  $\begin{array}{c}\text{D=}\frac{1}{4}+\frac{7}{16}\\ \text{D}=\frac{4+7}{16}\\ \text{D}=\frac{11}{16}\text{in}\end{array}$

Substitute $\frac{59}{64}\text{in}$ for $\text{B}$, $\frac{25}{16}\text{in}$ for $\text{C}$ and $\frac{11}{16}\text{in}$ for $\text{D}$ in equation (5).

  $\begin{array}{c}\text{E=}\frac{59}{64}+\frac{25}{16}+\frac{11}{16}\\ \text{E}=\frac{59+100+44}{64}\\ \text{E}=\frac{203}{64}\text{in}\\ \text{E}=3\frac{11}{64}\text{in}\end{array}$

Substitute $\frac{21}{64}\text{in}$ for $zk$, $\frac{5}{16}\text{in}$ for $ml$ and $\frac{11}{64}\text{in}$ for $no$ in equation (6).

  $\begin{array}{c}\text{F=}\frac{21}{64}+\frac{5}{16}+\frac{11}{64}\\ \text{F}=\frac{21+20+11}{64}\\ \text{F}=\frac{52}{64}\text{in}\\ \text{F}=\frac{13}{16}\text{in}\end{array}$

Thus, the length of A, B, C, D, E and F of the part are $1\frac{1}{16}\text{in}$, $\frac{59}{64}\text{in}$, $1\frac{9}{16}\text{in}$, $\frac{11}{16}\text{in}$, $3\frac{11}{64}\text{in}$ and $\frac{13}{16}\text{in}$ respectively.

Conclusion:

The length of A, B, C, D, E and F of the part are $1\frac{1}{16}\text{in}$, $\frac{59}{64}\text{in}$, $1\frac{9}{16}\text{in}$, $\frac{11}{16}\text{in}$, $3\frac{11}{64}\text{in}$ and $\frac{13}{16}\text{in}$ respectively.