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) In your final answers, include all formulas, equations, and calculations necessary to determine the correct answers.

Answer 1

Pls. see attachment.

Answer 2

Answer:

The total cost of the rocks needed for the border is $538.80.

Step-by-step explanation:

The length of the lawn is = 150 feet

The width of the lawn is = 80 feet

The gravel border will be 6 feet wide from all sides.

So, bigger rectangle will have length = $150+12=162$ feet

And width will be = $80+12=92$ feet

Area of the bigger rectangle = $162\times92=14904$ square feet

Area of the smaller rectangle = $150\times80=12000$ square feet

So, area of the gravel area will be = $14904-12000=2904$ square feet.

Now depth of gravel is 2 inches. So, volume will be area of gravel times depth.

We will convert 2 inches in feet.

12 inches = 1 feet

So, 2 inches = $\frac{2}{12}=0.167$ feet

$2904\times0.167=484.97$ cubic feet

1 cubic foot = 0.037037 cubic yard

So, 484.97 cubic feet = $484.97\times0.037037=17.96$ cubic yards

Now cost of gravel per cubic yard is $30.

So, total cost will be = $30\times17.96=538.80$ dollars

Therefore, the total cost of the rocks needed for the border is $538.80.

Please find attached the diagram of the lawn.