Chapter 1.5, Problem 39E

(a)

To determine

To write: the formula of circumference of a circle.

Answer to Problem 39E

  $C=2\pi r$

Explanation of Solution

Circumference of a circle is given by formula,

  $C=2\pi r$ ,

Where r = radius of the circle

(b)

To determine

To find: the radius of column if the circumference is 7 feet, 8 feet and 9 feet.

Answer to Problem 39E

When C=7 feet, then r = 1.11 feet

When C=8 feet, then r = 1.27 feet

When C=9 feet, then r = 1.43 feet

Explanation of Solution

Given information: A figure is given as follows-

  

In which column is one type of cylindrical stone.

Since C= 7 feet, then putting this value in above formula, $C=2\pi r$

  $\begin{array}{l}2\pi r=7\\ \Rightarrow 2\times \frac{22}{7}\times r=7\text{ {since }\pi \text{=}\frac{22}{7}\}\\ \Rightarrow r=\frac{7\times 7}{22\times 2}=\frac{49}{44}=1.11\text{ {upto the two places of decimals}}\end{array}$

Rounding off to the nearest tenth, r = 1.1 feet

Similarly, when C= 8 feet, then putting this value in above formula, $C=2\pi r$

  $\begin{array}{l}2\pi r=8\\ \Rightarrow 2\times \frac{22}{7}\times r=8\text{ {since }\pi \text{=}\frac{22}{7}\}\\ \Rightarrow r=\frac{7\times 8}{22\times 2}=\frac{56}{44}=\frac{14}{11}\text{=1}\text{.27 {upto the two places of decimals}}\end{array}$

Rounding off to the nearest tenth, r = 1.3 feet

Similarly, when C= 9 feet, then putting this value in above formula, $C=2\pi r$

  $\begin{array}{l}2\pi r=9\\ \Rightarrow 2\times \frac{22}{7}\times r=9\text{ {since }\pi \text{=}\frac{22}{7}\}\\ \Rightarrow r=\frac{7\times 9}{22\times 2}=\frac{63}{44}=1.43\text{ {upto the two places of decimals}}\end{array}$

(c)

To determine

To explain: how to calculate area of cross-section of column if circumference of column is given.

Explanation of Solution

To find the area of cross-section of column when circumference is given follows the following steps-

1. First calculate the radius r from formula $C=2\pi r$
2. Then put this value of r in the formula of area of cross-section of column, $\text{A=}\pi {\text{r}}^2$ and calculate area of cross section of column.