Chapter 4.1, Problem 53E

Solution

a.

To identify: The height of which the object is lifted if $r=4in,\theta =720°$ the given radius r used to lift heavy object is positioned 10 ft above ground level.

  

The height to which the object is lifted when radius $r=4$ inches and $\theta =720°$ is 50.265 inches.

Given information:

It is given that $r=4in\text{ and }\theta =720°$ .

Explanation:

Consider the given information.

Recall that $s=\frac{\pi r\theta }{180}$ where r is the radius of the circle and $\theta$ is the central angle.

Thus,

  $\begin{array}{c}s=\frac{3.14\times 4\times 720°}{180°}\\ =16\pi \\ =50.265\text{ inches}\end{array}$

Here, the height to which the object is lifted when radius $r=4$ inches and $\theta =720°$ is 50.265 inches.

b.

To identify: The height to which the object is lifted where $r=2in,\text{ and }\theta °=180°$ .

The height to which the object is lifted when radius $r=2$ inches and $\theta =180°$ is 6.283 inches.

Given information:

The given is $r=2in,\text{ and }\theta °=180°$

Explanation:

Consider the given information.

Recall that $s=\frac{\pi r\theta }{180}$ where r is the radius of the circle and $\theta$ is the central angle.

Thus,

  $\begin{array}{c}s=\frac{3.14\times 4\times 180°}{180°}\\ =2\pi \\ =6.283\text{ inches}\end{array}$

Here, the height to which the object is lifted when radius $r=2$ inches and $\theta =180°$ is 6.283 inches.