Chapter 0.8, Problem 8E

To determine

To calculate: The area of a quarter circle with diameter 4 meters.

Answer to Problem 8E

The area of the circle is $\text{3}{\text{.1 m}}^{\text{2}}$ .

Explanation of Solution

Given information:

A quarter circle with diameter 4 meters.

Formula used:

Area $\left(A\right)$ of a quarter circle with radius r is given by $A=\frac{\pi r^2}{4}$ .

Calculation:

Consider the provided statement a quarter circle with diameter 4 meters.

Since, radius is half of diameter, so, radius of quarter circle is 2 meters.

Recall that area $\left(A\right)$ of a quarter circle with radius r is given by $A=\frac{\pi r^2}{4}$ .

Apply it,

  $\begin{array}{c}A=\frac{\pi r^2}{4}\\ =\frac{3.14\times 2^2}{4}\\ =\frac{3.14\times 4}{4}\\ =\text{3}{\text{.14 m}}^{\text{2}}\end{array}$

Rounding off to the nearest tenth, we get,

  $A=\text{3}{\text{.1 m}}^{\text{2}}$

Thus, the area of the quarter circle is $\text{3}{\text{.1 m}}^{\text{2}}$ .