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?
Accepted Solution
A:
Answer:5.77 mStep-by-step explanation:The swimming pool has a rectangle in the center of dimension 10 m by 8 m and two semicircles at each end.
So, the area of the floor of the pool will be
[tex](10 \times 8) + \frac{\pi (4)^{2} }{2} + \frac{\pi (4)^{2} }{2} =130.28[/tex] m²
Now, the perimeter of the pool is [tex]\frac{2 \times \pi \times (4) }{2} + \frac{2 \times \pi \times (4) }{2} + 2 \times 10 = 45.1428[/tex] m.
Now, it is given that the paved area around the pool is double the area of the pool.
If the width of the paved area is x m then 45.1428x = 2 × 130.28
⇒ x = 5.77 m (Answer)