A rectangular pool's depth is 1m at the shallow end and gradually increases to 4m at the deep end. The pool is 32m in length and 12m width.

1. calculate the total surface area (m squared) of the pool.
2. The cost of painting the pool at $5 per square foot.
3. the amount of water(litres) required to fill the pool.

SA is the rectangular base + 2ends + 2trapezpoids

for the length of the slanted base we need to use Pythagoras

H^2 = 32^2 + 3^2
h = √1033

area of base = 12√1033
area of each trapezoid
= 32(1+4)/2 = 80
short end = 12
deep end = 48

Total surface area = 12√1033 + 2(80) + 12 + 48
= 605.684 m^2

b) I will assume you meant $5 per square metre
cost = 5(above surface area)

c) I will consider one of the traps as the base
Volume = 80(12) = 960 m^3
= 960 000 litres

To calculate the total surface area of the pool, we need to determine the areas of the front side, back side, two ends, and the bottom.

1. Front and Back Sides:
The front and back sides of the pool have the same dimensions — length and depth. To calculate the area, we multiply the length by the average depth of the pool (since it gradually increases from 1m to 4m).

Average Depth = (1m + 4m) / 2 = 2.5m

Area of Front/Back Side = Length × Average Depth
= 32m × 2.5m
= 80m² (square meters)

2. Two Ends:
The two ends are rectangular in shape and have a height of 4m and the width of 12m. Thus, to calculate the area:

Area of Two Ends = 2 × Height × Width
= 2 × 4m × 12m
= 96m²

3. Bottom:
The bottom of the pool is a rectangle with dimensions equal to the length and width of the pool. Therefore:

Area of Bottom = Length × Width
= 32m × 12m
= 384m²

Total Surface Area of the Pool = 2 × (Area of Front/Back Side) + (Area of Two Ends) + (Area of Bottom)
= 2 × 80m² + 96m² + 384m²
= 640m² + 96m² + 384m²
= 1120m²

So, the total surface area of the pool is 1120 square meters.

Now, let's calculate the other details:

2. Cost of Painting the Pool:
To calculate the cost of painting the pool, we need to convert the surface area from square meters to square feet, as the cost is given in dollars per square foot.

1 square meter = 10.764 square feet (approximately)

Cost of Painting the Pool = Total Surface Area × Cost per Square Foot
= 1120m² × $5/10.764ft²
≈ $520.36

Therefore, the cost of painting the pool would be approximately $520.36.

3. Amount of Water Required to Fill the Pool:
To calculate the volume of the pool in liters, we need to multiply the area of the pool's cross-section by its length.

Cross-sectional Area = (Width × Average Depth)
= 12m × 2.5m
= 30m²

Volume of Pool = Cross-sectional Area × Length
= 30m² × 32m
= 960m³

1 cubic meter = 1000 liters

Volume of Pool in Liters = 960m³ × 1000 liters/m³
= 960000 liters

Therefore, approximately 960,000 liters of water would be required to fill the pool.