Chapter 0, Problem 51POT

To determine

To find:the circumference and the area of the given circle as shown in the given figure. Round to the nearest tenth.

Answer to Problem 51POT

  $c=78.60\text{ inch and }A=491.1{\text{ inch}}^2$ .

Explanation of Solution

Given:

The given figure is

Concept used:

Circumference of the circle is $c=\pi d=2\pi r$

Area of the circle is $A=\pi r^2$ .

Calculation:

According to the figure, the diameter is $d=25\text{inch}$ .

Therefore, radius is $r=\frac{d}{2}=\frac{25}{2}\text{inch}$ .

Now, circumference of the circle is given by

  $\begin{array}{l}c=\pi d\\ =\frac{22}{7}\times 25\\ =\frac{550}{7}\\ =78.55\text{ inch}\\ =78.60\text{ inch}\{\text{round up to nearest tenth}}\end{array}$

Again, area of the circle is given by

  $\begin{array}{l}A=\pi r^2\\ =\frac{22}{7}\times {\left(\frac{25}{2}\text{ inch}\right)}^2\\ =\frac{22}{28}\times 625{\text{ inch}}^2\\ =491.071{\text{ inch}}^2\\ =491.1{\text{ inch}}^2\{\text{round up to nearest tenth}}\end{array}$

Hence, the circumference and the area of the given circle is $c=78.60\text{ inch and }A=491.1{\text{ inch}}^2$ .