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Problem 849

# A $$20 \times 40$$ -ft. swimming pool is $$4 \mathrm{ft}$$. deep and is filled to the brim, a) How many cubic feet of water are in the pool? b) If one gallon is $$0.13$$ cubic feet, how many gallons of water are in the pool? c) If water weighs approximately $$62.4 \mathrm{lb} / \mathrm{cu}$$. ft., what is the approximate weight of water in the pool?

Expert verified
The swimming pool has a volume of 3,200 cubic feet, contains approximately 24,615 gallons of water, and the water weighs approximately 199,680 pounds.
See the step by step solution

## Step 1: Calculate the volume of the pool

To find the volume of the pool, we multiply its length, width, and depth. The equation for volume is: $$V=L \cdot W \cdot D$$ Where V is the volume, L is the length, W is the width, and D is the depth.: $$V = (20 ft) \times (40 ft) \times (4 ft)$$

## Step 2: Evaluate the volume of the pool

Now, we substitute the given values into the equation and find the volume: $$V = (20 ft) \times (40 ft) \times (4 ft) = 3,200 \, ft^3$$ So, there are 3,200 cubic feet of water in the pool.

## Step 3: Convert cubic feet to gallons

We are given that one gallon of water is equal to 0.13 cubic feet. To find the number of gallons, we divide the volume in cubic feet by 0.13: Gallons = $$\frac{\text{Cubic Feet}}{0.13} = \frac{3,200}{0.13}$$

## Step 4: Evaluate the number of gallons of water

Now, we calculate the number of gallons of water in the pool: Gallons = $$\frac{3,200}{0.13} \approx 24,615$$ So, there are approximately 24,615 gallons of water in the pool.

## Step 5: Calculate the weight of the water in the pool

We are given that the water weighs 62.4 lb/cubic foot. To find the weight of the water, we multiply the volume in cubic feet by the weight per cubic foot: Weight = (Cubic Feet) × (Weight per Cubic Foot) = $$3,200 \, ft^3 \times 62.4 \, \frac{lb}{ft^3}$$

## Step 6: Evaluate the weight of the water in the pool

Now, we calculate the weight of the water in the pool: Weight = $$3,200 \, ft^3 \times 62.4 \, \frac{lb}{ft^3} = 199,680 lb$$ So, the approximate weight of the water in the pool is 199,680 pounds.

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