A contractor has been asked to pave 15 miles of new road. Before he can set his price, he needs to know how much the cement will cost. If the road is 45 feet wide and 9 inches thick and the cost of cement is $35 per cubic yard, what will be the cost of the cement needed for the road?
Convert all to common units, in this case, yards.
45' = 15 yds
9" = .25 yds
1 mile = 1760 yds
15 * .25 * 1760 * 15 * $35 = ?
To calculate the cost of the cement needed for the road, we need to determine the volume of cement required first. Let's break down the solution step by step:
1. Convert the measurements to a consistent unit: Since the width is given in feet and the thickness in inches, let's convert everything to feet. There are 5280 feet in a mile, so the width of the road is 45 feet and the thickness is 9 inches, which is equal to 0.75 feet (since there are 12 inches in a foot).
2. Calculate the volume of the road: The volume of the road can be calculated by multiplying the width, thickness, and length. Since the length of the road is given as 15 miles, we need to convert it to feet by multiplying by 5280. So, the volume can be calculated as follows: Volume = width × thickness × length.
Volume = 45 feet × 0.75 feet × (15 miles × 5280 feet/mile)
Volume = 45 feet × 0.75 feet × 79,200 feet
Volume = 2,838,000 cubic feet
3. Convert the volume to cubic yards: Since the cost is given per cubic yard, let's convert the volume from cubic feet to cubic yards. There are 27 cubic feet in a cubic yard. So, we divide the volume by 27 to get the volume in cubic yards.
Volume in cubic yards = 2,838,000 cubic feet / 27 cubic feet/yard
Volume in cubic yards = 105,111.11 cubic yards (rounded to two decimal places)
4. Calculate the cost of the cement: The cost of cement is given as $35 per cubic yard. Multiply the volume of cement needed by the cost per cubic yard to find the total cost.
Cost of cement = Volume in cubic yards × Cost per cubic yard
Cost of cement = 105,111.11 cubic yards × $35/cubic yard
Cost of cement = $3,678,888.89
Hence, the estimated cost of the cement needed for the road is approximately $3,678,888.89.