Chapter 11.6, Problem 6PSA

a.

To determine

To find: The total area watered.

Answer to Problem 6PSA

The total area wateredis $57m^2$ .

Explanation of Solution

Given:

Circles with center O and center X of radius 3 m are watered by sprinklers in a rectangular lawn.

Formula Used:

Area of circle: $A=\pi r^2$

r = radius of acircle.

Calculation:

  

Area of circle: $A=\pi r^2$

Area of circle with center O is similar to area of circle with center X .

Area of circle O is as follows:

  $\begin{array}{l}r=3\\ A=\pi r^2\\ $ A=\pi {(3)}^2$A=9\pi \end{array}$

Area of circle with center O is similar to area of circle with center X .

Total area watered= Area of circle with center O + Area of circle with center X

  $\begin{array}{l}=9\pi +9\pi \\ =18\pi \end{array}$

  $\approx 57m^2$

b.

To determine

To calculate: The area of whole lawn.

Answer to Problem 6PSA

The area of whole lawn is $72m^2$ .

Explanation of Solution

Given:

Circles with center O and center X of radius 3 m are watered by sprinklers in a rectangular lawn.

Formula Used:

  $\begin{array}{l}Areaofrectangle=b\ast h\\ b=Base,\\ h=Height\end{array}$

Calculation:

  

  $\begin{array}{l}h=r+r+r+r\\ h=3+3+3+3\\ h=12\\ b=r+r\\ b=3+3\\ b=6\\ A=b\ast h\\ A=6*12\\ A=72mete{r}^2\end{array}$

c.

To determine

To find: The area of lawn not watered.

Answer to Problem 6PSA

The area of lawn not wateredis $15m^2$ .

Explanation of Solution

Given:

Circles with center O and center X of radius 3 m are watered by sprinklers in a rectangular lawn.

Area of rectangle $=72mete{r}^2$

Area watered $=57mete{r}^2$

Formula Used:

Area of the lawn not watered (Shaded Area) = Area of rectangle - Area watered.

Calculation:

  

Area of the lawn not watered (Shaded Area) = Area of rectangle - Area watered

Shaded Area $=72-57=15m^2$