Question

a farmer has farmland that is a rectangle 3 km long and 2.5 km wide. he wants to completely cover the farmland in dirt. he knows the area each truckload of dirt covers, but only in square miles.
(a) find the area of the farmland in square miles. do not round intermediate computations and round your final answer to two decimal places. use the table of conversion facts, as needed.
(b) the farmer wants to cover his farmland with dirt. he doesnt have any to begin with and he cant buy partial truckloads of dirt. each truckload of dirt covers 0.8 mi². how many whole truckloads of dirt does the farmer need to buy to completely cover his farmland?
(c) if each truckload of dirt costs $65.18, how much will he need to spend on dirt? write your answer to the nearest cent.
conversion facts for length
1 inch (in) = 2.54 centimeters (cm)
1 foot (ft) = 30.48 centimeters (cm)
1 yard (yd) = 0.91 meters (m)
1 mile (mi) ≈ 1.61 kilometers (km)
note that \≈\ means \is approximately equal to\. for this problem, treat ≈ as if it were =.

Explanation:

Step1: Calculate the area of the farmland in square - kilometers

The farmland is a rectangle with length $l = 3$ km and width $w = 2.5$ km. The area formula for a rectangle is $A=l\times w$. So, $A = 3\times2.5=7.5$ km².

Step2: Convert square - kilometers to square - miles

We know that $1$ mile $\approx1.61$ km. So, $1$ km $\approx\frac{1}{1.61}$ miles. Then, $1$ km² $\approx(\frac{1}{1.61})^2$ mi².
To convert $7.5$ km² to mi², we multiply by the conversion factor: $A_{mi^2}=7.5\times(\frac{1}{1.61})^2$.
$A_{mi^2}=7.5\times\frac{1}{2.5921}\approx2.89$ mi².

Step3: Calculate the number of truckloads

Each truckload covers $0.8$ mi². Let $n$ be the number of truckloads. Then $n=\frac{A_{mi^2}}{0.8}=\frac{2.89}{0.8}=3.6125$. Since the farmer can't buy partial truckloads, he needs to buy $4$ truckloads.

Step4: Calculate the cost

Each truckload costs $\$65.18$. The total cost $C$ is $C = 4\times65.18=\$260.72$.

Answer:

(a) $2.89$ mi²
(b) $4$ truckloads
(c) $\$260.72$