A sidewalk is to be constructed around a swimming pool that measures (11.00+/-0.12) m by (17.40+/-0.12) m. If the sidewalk is to measure (1.22+/-0.02) m wide by (9.60+/-0.15) cm thick, what volume of concrete is needed?
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To calculate the volume of concrete needed for the sidewalk around the swimming pool, we need to multiply the area of the sidewalk by its thickness.
First, let's calculate the area of the sidewalk. The dimensions of the swimming pool are given as (11.00+/-0.12) m by (17.40+/-0.12) m, and the sidewalk is (1.22+/-0.02) m wide. To find the width of the sidewalk around the pool, we subtract twice the sidewalk width from each side of the pool:
Width of the sidewalk = Width of the pool + 2 × Sidewalk width
= (11.00+/-0.12) m + 2 × (1.22+/-0.02) m
Similarly, we calculate the length of the sidewalk by adding twice the sidewalk width to each end of the pool:
Length of the sidewalk = Length of the pool + 2 × Sidewalk width
= (17.40+/-0.12) m + 2 × (1.22+/-0.02) m
Now, we can calculate the area of the sidewalk:
Area of the sidewalk = Width of the sidewalk × Length of the sidewalk
Next, we need to calculate the volume of the concrete. The thickness of the sidewalk is given as (9.60+/-0.15) cm, which needs to be converted to meters:
Thickness of the sidewalk = (9.60+/-0.15) cm ÷ 100
Finally, we can calculate the volume of concrete needed:
Volume of concrete = Area of the sidewalk × Thickness of the sidewalk
Make sure to substitute the actual values, including the uncertainty ranges, into the calculations to obtain the final volume of concrete needed.