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. 2.89 mi² (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? 4 truckloads (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. $260.72

Explanation:

Step1: Convert area of farmland from square - km to square - miles

1 km = 0.621371 miles, so 1 km²=(0.621371)² mi²≈0.386102 mi².
The area of the farmland A = 3 km×2.5 km = 7.5 km².
Converting to square - miles: A = 7.5×0.386102 mi²≈2.895765 mi²≈2.90 mi².

Step2: Calculate number of truckloads

Each truckload covers 0.8 mi².
Let the number of truckloads be n. Then n=\frac{2.895765}{0.8}=3.61970625.
Since the farmer can't buy partial truckloads, he needs to buy 4 truckloads.

Step3: Calculate total cost

Each truckload costs $65.18.
The total cost C = 4×$65.18=$260.72.

Answer:

(a) 2.90 mi²
(b) 4 truckloads
(c) $260.72