A concrete sidewalk is to be be built around the outside of the corner lot that measures 140ft by 180 ft. The side walk is to be 5ft wide. What is the surface area of the side walk? The side walk is to be 4 in. Thick. How many cubic yards of concrete are needed? How much will it cost at $90/yd^3?
The correct answer and explanation is:
Solution:
- Find the Surface Area of the Sidewalk
- The sidewalk surrounds a rectangular lot measuring 140 ft × 180 ft.
- The sidewalk is 5 ft wide, so the outer dimensions of the whole sidewalk structure become:
[
(140 + 2(5)) \times (180 + 2(5)) = 150 \times 190
] - The area of the outer rectangle (lot + sidewalk):
[
150 \times 190 = 28,500 \text{ ft}^2
] - The area of the inner rectangle (lot only):
[
140 \times 180 = 25,200 \text{ ft}^2
] - The surface area of the sidewalk:
[
28,500 – 25,200 = 3,300 \text{ ft}^2
]
- Find the Volume of Concrete Needed
- The sidewalk is 4 inches thick, which is ( \frac{4}{12} = \frac{1}{3} ) ft.
- Volume of the sidewalk:
[
3,300 \times \frac{1}{3} = 1,100 \text{ ft}^3
] - Convert to cubic yards (1 cubic yard = 27 cubic feet):
[
\frac{1,100}{27} \approx 40.74 \text{ yd}^3
]
- Find the Total Cost
- The cost per cubic yard is $90:
[
40.74 \times 90 = 3,666.60
] - Total cost: $3,666.60
Explanation:
To build the sidewalk, we first determine its surface area by finding the difference between the outer rectangle (sidewalk + lot) and the inner rectangle (lot only). Then, by multiplying this area by the thickness of the sidewalk in feet, we find the total volume of concrete needed. Converting this volume into cubic yards allows us to determine the total cost at the given rate of $90 per cubic yard. This ensures an accurate estimate for material costs in constructing the sidewalk.
Now, let’s generate an image illustrating this sidewalk.
Here is the generated diagram illustrating the lot and sidewalk with labeled dimensions. Let me know if you need any modifications or further explanations!
