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 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)

Answer 1

A) Diagram

Below is a sketch of the recctangular lawn (the inside rectangle) and the gravel border.


  6 ft + 150 yards + 6 ft
-------------------------------
|                                    |
|     ---------------------      |
|     |                        |     |
|     |                        |     |   6 ft + 80 yard + 6 ft
|     |                        |     |
|      ---------------------     |
|                                    |
|------------------------------|

B) How many square feet of the gravel will surround the lawn?

Conversion: 1 yard = 3 feet

=> 80 yard = 80*3 feet = 240 feet

=> 150 yard = 150 * 3 feet = 450 feet

Area of the external rectangle = (6 ft + 240 ft + 6 ft) (6 ft + 450 ft + 6 ft) = 252 ft * 462 ft = 116,424 ft^2

Area of the internal rectangle = 240 ft * 450 ft = 108,000 ft^2

Area of the gravel border = 116,424 ft^2 - 108,000 ft^2 = 8424 ft^2

answer: 8424 ft^2

C) volume

volume = area of the base * depth

2 inches = 2/12 ft = 1/6 ft

=> volume = 8424 ft^2 * 1/6 ft = 1404 ft^3

answer: 1404 ft^3

C) cost

1 yard^3 = $ 30

1yard ^3 = (3 feet)^3 = 27 ft^3

=> cost = $ 30 / 27 ft^3

=> 1404 ft^3 * $30 / 27 ft^3 = $ 1560

answer: $ 1560