Chapter 14.1, Problem 20PSB

a.

To determine

To sketch the locus of points at a given distance.

Explanation of Solution

Given:

The point is $5$ units from a segment PQ.

Calculation:

The following is the sketch of the locus of the point is $5$ units from a segment PQ

  

b.

To determine

To find the area of locus sketched in part (A).

Answer to Problem 20PSB

  $60+25\pi$ square unit.

Explanation of Solution

Given:

The point is $5$ units from a segment PQ $=6$ .

Calculation:

Area is a rectangle plus two halves of a circle.

  $\begin{array}{l}A=\pi r^2+lw\\ =\pi {(}^5+10(6)\\ =60+25\pi \end{array}$

c.

To determine

To sketch the locus in space of the points.

Answer to Problem 20PSB

The shape is like that of a pill.

Explanation of Solution

Given:

The point is $5$ units from a segment PQ.

Calculation:

Rotate the 2D locus about the axis of the line segment, to obtain a 3D "pill"-shaped hollow object.

d.

To determine

To find the volume of locus sketched in part (C) if PQ $=6$

Answer to Problem 20PSB

  $V=\frac{7}{3}\left(125\pi \right)$ cubic unit.

Explanation of Solution

Given:

The point is $5$ units from a segment PQ.

Calculation:

Add volume of cylinder in middle with two halves of spheres on the end.

  $\begin{array}{l}V=\frac{4}{3}\pi r^{2}h+\pi r^{2}h\\ V=\frac{4}{3}125\pi +125\pi \\ V=\frac{7}{3}\left(125\pi \right)\end{array}$