Final answer:
a) The perpendicular distance between two trapezoids of the pool is approximately 58.4 cm. None of the given options is correct
b) The total surface area of the pool is 6954.24 cm². None of the given options is correct
c) The amount of paint needed to paint the internal sides of the pool is 1393.92 liters. None of the given options is correct
d) The cost of 279 buckets of paint is $3,497.45.None of the given options is correct
Step-by-step explanation:
a) The average depth can be found by adding the deep end and shallow end depth and dividing by 2:
Average depth = (2.8 cm + 50 cm)/2 = 26.4 cm
Next, we can calculate the total volume of the pool using the formula for the volume of a trapezoid-shaped pool:
Volume = 3025 cm³ = 1/2 * (base₁+ base₂) * height * length
Plugging in the values we know:
3025 cm³ = 1/2 * (2.8 cm + 50 cm) * 26.4 cm * length
Simplifying the equation:
- 1.4 cm + 25 cm = length
- 26.4 cm * length = 3025 cm³
- length = 3025 cm³/26.4 cm ≈ 114.8 cm
Finally, we can calculate the perpendicular distance between the trapezoids:
Perpendicular distance = length/2 - (2.8 cm + 26.4 cm/2) = 114.8 cm/2 - 16 cm ≈ 58.4 cm
The perpendicular distance between two trapezoids of the pool is approximately 58.4 cm.
None of the given options is correct
b)To calculate the total surface area of the swimming pool, we need to find the areas of the trapezoid-shaped ends and the rectangular sides.
Find the area of the rectangular sides:
- - The length of one side is the distance between the deep end and the shallow end of the pool, which is 50 cm - 2.8 cm = 47.2 cm.
- - The height is the depth of the pool, which is 47.2 cm.
- - Use the formula A = length * height to calculate the area of each rectangular side:
- A = 47.2 cm * 47.2 cm = 2227.84 cm².
- - Since there are two sides, the total area of the rectangular sides is 2 * 2227.84 cm² = 4455.68 cm².
Calculate the total surface area of the pool:
- Add the area of the trapezoid-shaped ends to the area of the rectangular sides:
Total surface area = 2498.56 cm² + 4455.68 cm² = 6954.24 cm².
Therefore, the total surface area of the swimming pool is 6954.24 cm².
None of the given options is correct
c)To calculate the amount of paint needed to paint the internal sides of the pool, we need to find the total surface area of the pool and then multiply it by the paint requirement.
First, let's find the lengths of the parallel sides of the trapezoid.
- Length at the deep end = 2.8 cm
- Length at the shallow end = 0.5 m = 0.5 m * 100 cm/m = 50 cm
Next, let's find the average length of the parallel sides.
- Average length = (Length at the deep end + Length at the shallow end) / 2
- Average length = (2.8 cm + 50 cm) / 2
- Average length = 52.8 cm / 2
- Average length = 26.4 cm
Now, we can calculate the area of each trapezoidal base.
- Area of a trapezoid = (Length of parallel side 1 + Length of parallel side 2) * Height / 2
- Area of each trapezoidal base = (2.8 cm + 50 cm) * 26.4 cm / 2
- Area of each trapezoidal base = 52.8 cm * 26.4 cm / 2
- Area of each trapezoidal base = 1393.92 square centimeters
Since there are two trapezoidal bases, the total area of the bases is 2 * 1393.92 square centimeters = 2787.84 square centimeters.
Now, let's calculate the amount of paint needed.
- Amount of paint = Total surface area of the pool * Paint requirement
- Amount of paint = 2787.84 square centimeters * 0.5 liters/square centimeter
- Amount of paint = 1393.92 liters
Therefore, the amount of paint needed to paint the internal sides of the pool is 1393.92 liters.
None of the given options is correct
d) We can calculate the area of each trapezoidal base.
- Area of a trapezoid = (Length of parallel side 1 + Length of parallel side 2) * Height / 2
- Area of each trapezoidal base = (2.8 cm + 50 cm) * 26.4 cm / 2
- Area of each trapezoidal base = 52.8 cm * 26.4 cm / 2
- Area of each trapezoidal base = 1393.92 square centimeters
Since there are two trapezoidal bases, the total area of the bases is 2 * 1393.92 square centimeters = 2787.84 square centimeters.
Now, let's calculate the amount of paint needed.
- Amount of paint = Total surface area of the pool * Paint requirement
- Amount of paint = 2787.84 square centimeters * 0.5 liters/square centimeter
- Amount of paint = 1393.92 liters
To determine the number of 5-liter buckets of paint needed, we divide the amount of paint by the capacity of each bucket.
- Number of buckets = Amount of paint / Capacity of each bucket
- Number of buckets = 1393.92 liters / 5 liters/bucket
- Number of buckets = 278.784 buckets
Since we cannot have a fraction of a bucket, we need to round up to the nearest whole number. Therefore, we need a total of 279 buckets of paint.
Finally, let's calculate the cost.
- Cost = Number of buckets * Cost per bucket
- Cost = 279 buckets * $12.55/bucket
- Cost = $3,497.45
Therefore, the cost of 279 buckets of paint is $3,497.45.
None of the given options is correct