An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 5 m and a depth of 1.9 m. Suppose water is pumped into the pool at a rate of 18 m3 per hour. How many hours will it take to fill the empty pool?Use the value 3.14 for π, and round your answer to the nearest hour. Do not round any intermediate computations.hour(s)
Question
An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 5 m and a depth of 1.9 m. Suppose water is pumped into the pool at a rate of 18 m3 per hour. How many hours will it take to fill the empty pool?Use the value 3.14 for π, and round your answer to the nearest hour. Do not round any intermediate computations.hour(s)
Solution
To solve this problem, we first need to calculate the volume of the pool. The volume V of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height (or depth in this case).
Step 1: Convert the diameter to radius. The radius is half of the diameter, so r = 5m / 2 = 2.5m.
Step 2: Substitute the values into the volume formula. V = π * (2.5m)² * 1.9m = 3.14 * 6.25m² * 1.9m = 37.68 cubic meters.
Step 3: Now, we know that the pool can be filled at a rate of 18 cubic meters per hour. So, to find out how long it will take to fill the pool, we divide the volume of the pool by the rate at which it can be filled. Time = Volume / Rate = 37.68m³ / 18m³/hour = 2.093 hours.
Step 4: Round the answer to the nearest hour. So, it will take approximately 2 hours to fill the pool.
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