Chapter 11.5, Problem 17PPS

(a)

To determine

To find: The way in which the radius changes when the area is doubled.

Answer to Problem 17PPS

The case when the area is doubled, then the radius is multiplied by the factor of $\sqrt{2}$ that is $33.9\text{in}$ .

Explanation of Solution

Given:

The given radius is $24\text{in}$ .

Calculation:

Consider the radius of the circle is $r$ and when the radius is doubled the radius is $2r$ .

Then, by the theorem of area of the similar polygon,

  $\begin{array}{l}{k}^2=\frac{2r}{r}\\ k=\sqrt{2}\end{array}$

Then, the radius is,

  $2\sqrt{2}=33.9\text{in}$

Thus, the case when the area is doubled, then the radius is multiplied by the factor of $\sqrt{2}$ that is $33.9\text{in}$ .

(b)

To determine

To find: The way in which the radius changes when the area is tripled.

Answer to Problem 17PPS

The case when the area is doubled, then the radius is multiplied by the factor of $\sqrt{3}$ and the radius is $41.6\text{in}$ .

Explanation of Solution

Given:

The given radius is $24\text{in}$ .

Calculation:

Consider the radius of the circle is $r$ and when the radius is tripled the radius is $3r$ .

Then, by the theorem of area of the similar polygon,

  $\begin{array}{l}{k}^2=\frac{3r}{r}\\ k=\sqrt{3}\end{array}$

Then, the radius is,

  $24\sqrt{3}=41.6\text{in}$

Thus, the case when the area is doubled, then the radius is multiplied by the factor of $\sqrt{3}$ and the radius is $41.6\text{in}$ .

(c)

To determine

To find: The way in which the radius changes when the area is increased by the factor $x$ .

Answer to Problem 17PPS

The way in which the radius changes when the area is increased by the factor $x$ is $24\sqrt{x}$ .

Explanation of Solution

Given:

The given radius is $24\text{in}$ .

Calculation:

Consider the radius of the circle is $r$ and when the radius is tripled the increase by the factor $x$ is $xr$ .

Then, by the theorem of area of the similar polygon,

  $\begin{array}{l}{k}^2=\frac{xr}{r}\\ k=\sqrt{x}\end{array}$

Then, the radius is,

  $24\sqrt{x}$

Thus, the way in which the radius changes when the area is increased by the factor $x$ is $24\sqrt{x}$ .