Chapter 11.8, Problem 19PPS

To determine

To compute the area that the sprinkler waters.

Answer to Problem 19PPS

  $434.6$ squarefeet.

Explanation of Solution

Given information:

Radius $r=12$ feet. This is the circular area’s radius that the sprinkler covers.

For rectangular flower bed within the sprinkler’s circular area, the length is $l=6$ feet and breadth is $b=3$ .

Formula used:

Area of circle $A=\pi \times r^2$ . Where ‘r’ is the radius.

Area of rectangle $r=l\times b$ . Where ‘l’ is the length and ‘b’ is the breadth.

Calculation:

To compute the area that the sprinkler covers, find the area of the circular part that in waters and subtract the rectangular flower bed from it.

  $A=\pi \times r^2$

Putting the value of ‘r’.

  $=\frac{22}{7}\times {12}^2$

Taken $\pi =\frac{22}{7}$

  $=\frac{22}{7}\times 144$

On simplifying the expression.

  $=\frac{3168}{7}$

Converting the fraction to decimal number.

  $=452.57$

Rounding to the nearest tenth.

  $=452.6$ square feet.

Area of the rectangular flower bed

  $r=l\times b$

Formula for area of rectangle.

  $=6\times 3$

Putting numeric values.

  $=18$ square feet.

Hence, the area the water sprinkler covers is

  $=a-r$

Subtracting the two areas.

  $=452.6-18$

On subtraction.

  $=434.6$ square feet.