The concrete for a sidewalk is being poured outside the perimeter of a new subdivision, which is a 280 ft. by 720 ft. rectangle. The building code requires that the sidewalk be 5 feet wide and 8 inches deep. How many cubic yards of concrete will need to be poured? How much will the concrete for the new subdivision cost if the price per cubic yard of concrete is $74.50 and an extra 5% of concrete is being ordered?
Dimensions of the rectangle including the sidewalk is
290 by 730 , (added 5 feet on each side)
surface area of sidwwalk
= 290x730 - 280x720
=10100 ft^2
volume of sidwwalk
= 10100(8/12) ft^3
= 20200/3 ft^3
but we are ordering 5% extra
volume ordered
= 20200/3 (1.05)
= 7070 cubic ft
= 7070/27 cubic yards
= 261.85 cubic yards
BUT we will probably have to order 262 yds^3
for a cost of
262(74.50)
= $19,519.00
$19,519.00
$19,519.000
19,000,000,00000,000EWAHGQHGO[V
To calculate the volume of concrete needed, we can first calculate the volume of the sidewalk and then subtract it from the volume of the rectangle.
1. Calculate the volume of the sidewalk:
The sidewalk is 5 feet wide and 8 inches deep. To convert the width to inches, we multiply by 12 (since there are 12 inches in a foot) - 5 feet x 12 inches/foot = 60 inches.
To convert the depth to feet, we divide by 12 (since there are 12 inches in a foot) - 8 inches / 12 inches/foot = 0.67 feet.
The volume of a rectangular prism is given by the formula V = length x width x height. So, the volume of the sidewalk is 280 ft x 720 ft x 0.67 ft = 135,360 ft³.
2. Calculate the volume of the rectangle:
The rectangle has dimensions of 280 ft x 720 ft x 8 inches.
To convert the depth to feet, we divide by 12 (since there are 12 inches in a foot) - 8 inches / 12 inches/foot = 0.67 feet.
So, the volume of the rectangle is 280 ft x 720 ft x 0.67 ft = 134,784 ft³.
3. Calculate the total volume of concrete:
The total volume of concrete needed is the volume of the rectangle minus the volume of the sidewalk: 134,784 ft³ - 135,360 ft³ = -576 ft³.
However, since the dimensions were given to the nearest whole number, there might be some rounding errors. In this case, we assume a negligible difference.
4. Calculate the extra 5% of concrete:
To account for any waste or errors, we need to order an extra 5% of concrete. We can calculate this by multiplying the total volume by 5% (0.05) and adding it to the total volume:
Extra volume = -576 ft³ x 0.05 = -28.8 ft³ (rounded to the nearest whole number)
Total volume with the extra 5% = -576 ft³ + -28.8 ft³ = -604.8 ft³
5. Calculate the concrete in cubic yards:
Since concrete is commonly measured in cubic yards, we need to convert the volume from cubic feet to cubic yards. There are 27 cubic feet in a cubic yard. Therefore, we divide the total volume by 27:
-604.8 ft³ / 27 ft³/yd³ = -22.4 yd³ (rounded to the nearest tenth)
So, the estimated volume of concrete needed is 22.4 cubic yards.
6. Calculate the cost of the concrete:
To find the cost of the concrete, we multiply the estimated volume by the price per cubic yard: 22.4 yd³ x $74.50/yd³ = $1,668.80
Therefore, the estimated cost of the concrete for the new subdivision is $1,668.80, including the extra 5% of concrete.