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Answer :
To solve the problem of how many gallons of water are needed to cover a hockey rink with 1.962 inches of water, we can follow these steps:
1. Convert the depth from inches to feet:
Since we know there are 12 inches in a foot, we divide the depth in inches by 12 to convert it to feet.
[tex]\[ \text{Water depth in feet} = \frac{1.962 \text{ inches}}{12} = 0.1635 \text{ feet} \][/tex]
2. Calculate the volume of water needed in cubic feet:
The volume is calculated by multiplying the area of the rink by the depth of the water in feet.
[tex]\[ \text{Volume in cubic feet} = 16330 \text{ square feet} \times 0.1635 \text{ feet} = 2669.955 \text{ cubic feet} \][/tex]
3. Convert the volume from cubic feet to gallons:
Using the conversion factor that 1 gallon is equivalent to 0.1337 cubic feet, we divide the total cubic feet by this factor to get the volume in gallons.
[tex]\[ \text{Volume in gallons} = \frac{2669.955 \text{ cubic feet}}{0.1337 \text{ cubic feet per gallon}} = 19969.75 \text{ gallons} \][/tex]
Therefore, approximately 19,969.75 gallons of water are needed to cover the hockey rink with 1.962 inches of water.
1. Convert the depth from inches to feet:
Since we know there are 12 inches in a foot, we divide the depth in inches by 12 to convert it to feet.
[tex]\[ \text{Water depth in feet} = \frac{1.962 \text{ inches}}{12} = 0.1635 \text{ feet} \][/tex]
2. Calculate the volume of water needed in cubic feet:
The volume is calculated by multiplying the area of the rink by the depth of the water in feet.
[tex]\[ \text{Volume in cubic feet} = 16330 \text{ square feet} \times 0.1635 \text{ feet} = 2669.955 \text{ cubic feet} \][/tex]
3. Convert the volume from cubic feet to gallons:
Using the conversion factor that 1 gallon is equivalent to 0.1337 cubic feet, we divide the total cubic feet by this factor to get the volume in gallons.
[tex]\[ \text{Volume in gallons} = \frac{2669.955 \text{ cubic feet}}{0.1337 \text{ cubic feet per gallon}} = 19969.75 \text{ gallons} \][/tex]
Therefore, approximately 19,969.75 gallons of water are needed to cover the hockey rink with 1.962 inches of water.
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