Chapter 0.8, Problem 20E

To determine

To calculate: The area of the circle with diameter 133 feet in which the art piece is placed.

Answer to Problem 20E

The area of the circle is $\text{13,898}{\text{.5 ft}}^{\text{2}}$ .

Explanation of Solution

Given information:

The piece of art is placed is placed in a traffic circle with diameter $133$ feet.

Formula used:

Area $\left(A\right)$ of a circle with radius r is given by $A=\pi r^2$ .

Calculation:

Consider the given statement that the piece of art is placed is placed in a traffic circle with diameter $133$ feet.

Since, radius is half of the diameter, so, radius is $\frac{133}{2}$ inches.

Recall that area $\left(A\right)$ of a circle with radius r is given by $A=\pi r^2$ .

Apply it,

  $\begin{array}{c}A=\pi r^2\\ =\frac{22}{7}\times \frac{133}{2}\times \frac{133}{2}\\ =13,898.5{\text{ft}}^{\text{2}}\end{array}$

Rounding off to the nearest tenth, we get,

  $A=13,898.5{\text{ ft}}^{\text{2}}$

Thus, the area of the circle is $\text{13,898}{\text{.5 ft}}^{\text{2}}$ .