Chapter 9.3, Problem 40PPE

Solution

(a)

To calculate: The scale factor that required to draw the pool in the paper.

To draw the pool the drawing should scale down by 2 with different units.

Given Information:

The given height of the pool is 52 in and the volume is $1100{\text{ft}}^3$ .

Formula Used:

Volume of a cylinder is $\pi r^{2}h$ .

Calculation:

It is given that the height of the pool is 52 in and the volume is $1100{\text{ft}}^3$ .

It is known that $1\text{ft}=12\text{in}$ .

Now, convert 52 in into foot.

  $\begin{array}{c}52\text{in}=\frac{52}{12}\\ \approx 4.33\text{ft}\end{array}$

Now, find the radius. Use the formula $\pi r^{2}h$ .

  $\begin{array}{c}\pi r^2\times 4.33=1100\\ \frac{22}{7}\times r^2\times 52=1100\\ r^2=\frac{1100\times 7}{4.33\times 22}\\ r\approx 8.99\end{array}$

Convert nearest to the tenth foot.

  $\text{radius}=9\text{ft}$

Now to draw this measurement in a diagram, the scale of the diagram must be same as the original pool.

That is scale should be equal to $\frac{9}{4.33}\approx 2$ .

Thus, drawing need to convert into some smaller units like cm, in.

Hence, to draw the pool the drawing should scale down by 2 with different units.

(b)

To find:Whether it needs to convert any of the measurement to different units.

Yes, it need.

Explanation:

Yes it needs to convert any of the measurement into a smaller units, which can fit to the paper.

Hence, yes.