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?
math:
Dimensions of the rectangle including the sidewalk is
290 by 730 , (added 5 feet on each side)
surface area of sidewalk
= 290x730 - 280x720
=10100 ft^2
volume of sidewalk
= 10100(8/12) ft^3
= 20200/3 ft^3
Final answer: 67333.3(repeating)
I think. I'm not sure.. I really need help. Can someone please help me with the math but explain it with words after it, too? Very confusing..
I agree with your method and with your answer
Make sure to divide your answer by 27 to make it in cubic yards
To find the volume of concrete needed for the sidewalk, we first need to calculate the surface area of the sidewalk.
The original dimensions of the rectangle are 280 feet by 720 feet. Adding 5 feet to each side for the sidewalk gives us new dimensions of 290 feet by 730 feet.
To find the surface area of the sidewalk, we subtract the area of the original rectangle from the area of the expanded rectangle.
Surface Area of Sidewalk = Area of Expanded Rectangle - Area of Original Rectangle
= (290 ft × 730 ft) - (280 ft × 720 ft)
= 211,700 ft² - 201,600 ft²
= 10,100 ft²
Now that we have the surface area, we can calculate the volume of the sidewalk.
The depth of the sidewalk is given as 8 inches. We need to convert this to feet by dividing by 12.
Volume of Sidewalk = Surface Area × Depth
= 10,100 ft² × (8/12) ft
≈ 6,733.33 ft³
To convert the volume from cubic feet to cubic yards, we divide by 27 since there are 27 cubic feet in a cubic yard.
Volume in Cubic Yards = Volume in Cubic Feet ÷ 27
= 6,733.33 ft³ ÷ 27
≈ 249.39 cubic yards
So, the final answer is approximately 249.39 cubic yards of concrete needed for the sidewalk.