Chapter 14.2, Problem 12PSC

a.

To determine

To find the locus in space of points that are 3 in. from a given plane and 5 in from a fixed plane.

Answer to Problem 12PSC

Two circles.

Explanation of Solution

Given:

The points are $3$ in. from a given plane and $5$ in from a fixed plane.

Calculation:

The locus of the points that are $3$ in. from a given plane and $5$ in from a fixed plane is described by below figure.

  

b.

To determine

To find the area of the figure found in part (a).

Answer to Problem 12PSC

  $32\pi$

Explanation of Solution

Given:

The points are $3$ in. from a given plane and $5$ in from a fixed plane.

Calculation:

The radius of the circle is $4$ inch.

Therefore the area of two circles is

  $\begin{array}{l}2\times \pi r^2\\ $ =2\pi {(4)}^2$=32\pi \end{array}$