A swimming pool size is 42 m long and 55 m wide with an average depth of 7.5 m. Using the density of water as 1 g/ml:
A. how many gallons of water fill the pool
B. The weight of water in lbs after the pool is full
C. How long will it take to fill the ppol if a pump fills the pool at a rate of 5.0 gal per min?
first you need to convert m^3 to gallons.
then, convert kg to lbs
To solve these questions, we need to follow the steps below:
A. Calculate the volume of the swimming pool in liters.
B. Convert the volume from liters to gallons.
C. Find the weight of water in pounds.
D. Determine the time required to fill the pool.
Let's go through each step:
A. Calculate the volume of the swimming pool in liters:
To find the volume, we use the formula:
Volume = Length x Width x Depth
Given:
Length = 42 m
Width = 55 m
Depth = 7.5 m
Volume = 42 m x 55 m x 7.5 m
Calculate the product: 42 x 55 x 7.5 = 17325 cubic meters
B. Convert the volume from liters to gallons:
1 liter is approximately equal to 0.264172 gallons.
So, multiply the volume in liters by 0.264172 to convert it to gallons.
Volume in gallons = 17325 cubic meters x 1000 liters/cubic meter x 0.264172 gallons/liter
Calculate: 17325 x 1000 x 0.264172 = 4585431.19 gallons
Therefore, approximately 4,585,431 gallons of water fill the pool.
C. Find the weight of water in pounds:
Given the density of water as 1 g/ml, we can use the following conversion factors:
1 gram = 0.00220462 pounds
1 milliliter = 0.033814 fluid ounces
So, to find the weight in pounds, we need to convert from gallons to milliliters, and then from milliliters to pounds.
Weight in pounds = Volume in gallons x 1000 milliliters/gallon x 0.033814 fluid ounces/milliliter x 0.00220462 pounds/gram
Calculate: 4585431.19 x 1000 x 0.033814 x 0.00220462 = 324310.64 pounds
Therefore, the weight of water in the pool, when full, is approximately 324,311 pounds.
D. Determine the time required to fill the pool:
Given that the pump fills the pool at a rate of 5.0 gallons per minute, we can divide the volume by the filling rate to get the time it takes.
Time in minutes = Volume in gallons / Filling rate in gallons per minute
Calculate: 4585431.19 gallons / 5.0 gallons per minute
Time in minutes = 917086.24 minutes
Therefore, it will take approximately 917,086 minutes (or approximately 637 days) to fill the pool.