A rectangular yard 102 feet long and 68 feet wide has some dead grass spots. The sprinkling system waters with 6 sprinklers. They water in a circle that touches the next circle, 3 on top and 3 on bottom. The radius each sprinkler covers is 17 feet.
Use pi = 3.14 and round your answers to one decimal place.

a. How much area does one sprinkler cover?
b. How much area do all 6 sprinklers cover?
c. What is the area of the lawn?
d. What area of the lawn is not watered?

Question

15-07-2018
Mathematics

contestada

A rectangular yard 102 feet long and 68 feet wide has some dead grass spots. The sprinkling system waters with 6 sprinklers. They water in a circle that touches the next circle, 3 on top and 3 on bottom. The radius each sprinkler covers is 17 feet.
Use pi = 3.14 and round your answers to one decimal place.

a. How much area does one sprinkler cover?
b. How much area do all 6 sprinklers cover?
c. What is the area of the lawn?
d. What area of the lawn is not watered?

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gordenfreemen38 gordenfreemen38 · Answer 1 · 2018-07-15T19:00:53+02:00

gordenfreemen38 gordenfreemen38

15-07-2018

a, Area of circle is pi*r^2

3.14(17)^2=907.46 feet^2

b, Multiply the area of one by six.

907.46*6=5444.76 feet^2

c, Length*width = 102*68 = 6936 feet^2

d, subtract area watered from area total

6936-5444.76=1491.24 feet^2

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RajarshiG RajarshiG · Answer 2 · 2022-07-07T12:24:10+02:00

As per the area of a circle, the area that one sprinkler covers is 907.46 square feet.

The area that all 6 sprinklers cover is 5444.76 square feet.

As per the area of a rectangle, the area of the lawn is 6936 square feet.

The area of the lawn is not watered is 1491.24 square feet.

What is the area of a rectangle?

The area of a rectangle is the product of the length and the width of the rectangle.

What is the area of a circle?

The area of a circle is the product of 'Pi'(π) and square of the radius of the circle.

Given, the rectangular yard 102 feet long and 68 feet wide.

The radius of each sprinkler is(r) 17 feet.

1. Therefore, the area covered by one sprinkler is

= π[tex]r^{2}[/tex] square unit

[tex]= (3.14)(17)^{2}[/tex] square feet

[tex]= 907.46[/tex] square feet

2. Total area covered by 6 sprinklers

[tex]= 6(907.46)[/tex] square feet

= 5444.76 square feet

3. The area of the lawn is

[tex]= (102)(68)[/tex] square feet

[tex]= 6936[/tex] square feet

4. The area of the lawn is not watered

[tex]= (6936-5444.76)[/tex] square feet

[tex]= 1491.24[/tex] square feet

Learn more about the area of a rectangle and a circle here: https://brainly.com/question/9337603

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