Respuesta :
Answer:
Water needed for pool = 486 cubic feet
Plastic liner required for the pool = 298.3 feet
Step-by-step explanation:
Top view of the pool is a composite figure, having one rectangle and a trapezoid.
1). Water needed for the pool = volume of the pool
Volume of the pool = Area of the base × Depth
= (Area of the rectangle + Area of the trapezoid)× depth
Area of the trapezoid = [tex]\frac{1}{2}(b_{1}+b_{2})\times h[/tex]
= [tex]\frac{1}{2}(11+9)\times (12-1.5)[/tex]
= 105 ft²
Area of the rectangle = Length × width
= 11 × 1.5
= 16.5 ft²
Now, volume of the pool = (105 + 16.5) × 4
= 121.5 × 4
= 486 cubic feet
b). Liner required = surface area of the pool excluding top
= Surface area of the walls + Area of the pool base
= (Perimeter of the pool) × depth + area of the base
= (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5
= 176.8 + 121.5
= 298.3 square feet
Therefore, amount of water required = 486 cubic feet
liner needed = 298.3 square feet
a. Water needed for pool = 486 cubic feet.
b. Plastic liner required for the pool = 298.3 feet.
Calculation of water needed and plastic liner required:
a.
Water needed for the pool = volume of the pool
Here
Volume of the pool = Area of the base × Depth
= (Area of the rectangle + Area of the trapezoid)× depth
So,
Area of the trapezoid = 0.5 × (b1 + b2) × h
= 0.5 × (11 + 9 )(12 -1.5)
= 105 ft²
Now the area of the rectangle
= Length × width
= 11 × 1.5
= 16.5 ft²
Now, volume of the pool = (105 + 16.5) × 4
= 121.5 × 4
= 486 cubic feet
b). Liner required = surface area of the pool excluding top
= Surface area of the walls + Area of the pool base
= (Perimeter of the pool) × depth + area of the base
= (12 + 11 + 1.5 + 10.7 + 9)×4 + 121.5
= 176.8 + 121.5
= 298.3 square feet
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