A company charges $42 per cubic yard of concrete. How much will it cost to pour a sidewalk that is 45 inches wide, 70 feet long, and 4 inches deep?
45" = 1.25 yards
70 feet = 23.333 yards
4 inches = 0.111 yards
1.25 * 23.33333 * 0.1111 * 42 = ?
To find out the cost of pouring the sidewalk, we need to calculate the volume of concrete required. Here's how we can solve the problem step by step:
Step 1: Convert the measurements to consistent units:
- Width: 45 inches = 45/12 = 3.75 feet
- Length: 70 feet (no conversion needed)
- Depth: 4 inches = 4/12 = 0.333 feet
Step 2: Calculate the volume of concrete:
The formula for calculating the volume of a rectangular prism is V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height.
In this case, the volume of the sidewalk can be calculated as:
Volume = 70 feet × 3.75 feet × 0.333 feet
Step 3: Calculate the cost:
The cost is given as $42 per cubic yard of concrete. We have the volume in cubic feet, so we need to convert it to cubic yards. Since 1 yard is equal to 3 feet, 1 cubic yard is equal to 3 × 3 × 3 = 27 cubic feet.
To convert the volume to cubic yards:
Volume (cubic yards) = Volume (cubic feet) / 27
Once we have the volume in cubic yards, we can calculate the total cost:
Total Cost = Volume (cubic yards) × Cost per cubic yard
Let's calculate it step by step:
Step 1:
Width = 3.75 feet
Length = 70 feet
Depth = 0.333 feet
Step 2:
Volume = 70 feet × 3.75 feet × 0.333 feet
Step 3:
Volume = 70 × 3.75 × 0.333 = 87.1875 cubic feet
Step 4:
Volume (cubic yards) = 87.1875 cubic feet / 27 = 3.229 cubic yards (rounded to 3 decimal places)
Step 5:
Total Cost = 3.229 cubic yards × $42/cubic yard
Total Cost = $135.57 (rounded to two decimal places)
Therefore, it will cost approximately $135.57 to pour the sidewalk.