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Answer :
Final answer:
The volume of water in the pool, calculated as 2/3 of the cylinder's volume and converted to gallons, is approximately 164 gallons.
Explanation:
To determine the volume of water in the pool, you need to calculate the volume of the cylinder and then figure out what 2/3 of that volume is.
The volume of a cylinder is given by the formula [tex]V = \pi r^2h[/tex], where r is the radius and h is the height. In this case, the diameter of the pool is 6 1/2 feet, which means the radius is half of that, or 3.25 feet. The height of our pool is 12 inches, which we need to convert to feet because our radius is in feet. 1 foot is equal to 12 inches, so 12 inches is equal to 1 foot.
Substituting these values into the formula, we get [tex]V = \pi (3.25)^2(1)[/tex]= approx. 33 cubic feet. However, the pool is only filled to 2/3 of its height, so the volume of the water is 2/3 * 33 = approx. 22 cubic feet.
Finally, we need to convert cubic feet to gallons. Since 1 cubic foot equals 7.48 gallons, 22 cubic feet equals roughly 164 gallons.
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Answer:
165.47≈165 Gallons of Water
Step-by-step explanation:
According To the Question,
- Given, A child-sized swimming pool can be modeled by a cylinder. The pool has a diameter of 6 1/2 feet (or) 6.5 feet (radius is 3.25 feet) and a height of 12 inches(1 feet).
The pool is filled with water to 2/3 of its height (H= 2/3 feet) .
Volume of Cylinder = π×R²×H , now put values, we get
Volume = 3.14×3.25²×2/3
Volume = 22.122 foot³ .
And, One cubic foot equals 7.48 gallons of water
Thus, 22.122 cubic foot equals to 165.47≈165 gallons of water .
