Question

Kamila has a rectangular lawn that measures 80 by 150 feet. She wants to lay gravel made from colored rock in a border, 6 feet wide, all around the lawn. Create a diagram that shows Kamila’s rectangular lawn and the gravel border. Assign variables to any unknown sides and label the diagram. Use your diagram to determine how many square feet of the gravel border will surround the lawn. Kamila decided that the depth of the gravel needs to be 2 inches. What is the total volume of gravel needed for the border? (Hint: dimensions must be in terms of the same unit before you can calculate the volume) D. A large bag of colored rock contains 5/8 of a cubic yard and costs $30. What is the total cost of the rocks needed for the border? (Hint: the volume of the border must be in terms of a cubic yard before you can calculate the cost) In your final answers, include all formulas, equations, and calculations necessary to determine the correct answers.

Answer 1

Answer:

1)Diagram attached

2)8424

3)1404

4)1569

Step-by-step explanation:

1)

Diagram is attached

2)

How many square feet of the gravel will surround the lawn:

Converting yards into feet:

1 yard =3 feet

So 80 yard =80(3) feet

                   =240 feet

and 150 yard =150 (3) feet

                     =450 feet

Area of rectangle is given by :length X width

Area of the outer border = (6+ 240+ 6 ) (6+ 450+6)

                                         = 252 X 462

                                         = 116424

Area of the lawn = 240 X 450

                            = 108000

Area of gravel border = 116424 - 108000

                                    = 8424

Area of gravel border is 8424 ft^2

3)

Total volume when depth is 2 inches:

converting inches to feet:

1 inch=  0.083 feet

2 inches =0.1667 feet

volume = base area X depth

            =8424 X 0.1667

            = 1404

 total volume of gravel needed for the border is 1404 ft^3

4)

Given:

A large bag of colored rock contains 5/8 of a cubic yard and costs $30

total cost of the rocks needed for the border=?

1 cubic yard = $30

converting cubic yard to cubic feet

1 cubic yard=27 cubic feet

cost of 1 cubic yard= cost of 27 cubic feet = $ 30

cost of 1 cubic feet=30/27

cost of  1404 cubic feet= 1404 X 30 / 27

                                     = 1560

the total cost of the rocks needed for the border is $1560!