A swimming pool is in the shape of a rectangle 10m by 8m with two semi circular ends. the paved area around the pool is of constant width. the paved area is double the area of the pool. what is the width of the paved area around the pool
Answers
Answer:
Width of the pavement is 2.13m.
Step-by-step explanation:
Area of the pool = (10×8) +(π×(8/2) ^2) =80+50.26=130.26 meter square.
Now circumference of the pool = 2×(10+8) +π×8 =36+25.13 =61.13m
Let the width of the pavement be X.
Therefore,
61.13× X = 130.26
X= (130.26/61.13) = 2.13 m.
width of the paved area around the pool = 4.415 m
Step-by-step explanation:
Assuming semi circle at 8 m width
Area of pool = 10 * 8 + 2 * (1/2) π (8/2)²
= 80 + 16π
Width of Paved area = w
Area including Paved area = (10)(8 + 2w) + 2 * (1/2)π( 4 + w)²
= 20w + 80 + π (w² + 16 + 8w)
Paved Area = 20w + 80 + π (w² + 16 + 8w) - (80 + 16π )
= 20w + π w² + 8 πw
Paved area = 2* Pool Area
=> 20w + π w² + 8 πw = 2 * (80 + 16π )
=> π w² + w(8 π + 20) - 2 * (80 + 16π ) = 0
We need to solve this to get Value of w
w² + 14.366w - 82.93 = 0
=> w = 4.415
width of the paved area around the pool = 4.415 m
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