The james family just put in a pool. It is 5 feet deep and has an 8 foot radius. They only want to fill the pool 5/6 of the way. What will be the volume of the pool once filled?
I'm so confused...please help.
V=πr^2h
V = 3.14 * 8^2 * 5
V = 1,004.8 cubic feet
(5/6) * 1.004.8 = _______ cubic feet
To find the volume of the pool, we can use the formula for the volume of a cylinder, which is given by V = πr^2h, where V represents volume, r represents radius, and h represents the height (or depth in this case) of the cylinder.
In this case, the pool has a radius of 8 feet and a depth of 5 feet. However, they only want to fill the pool 5/6 of the way, so we need to find 5/6 of the depth.
Depth of pool filled = 5/6 * 5 feet = (5/6) * 5 feet = 25/6 feet = 4.17 feet (rounded to two decimal places)
Now, we can substitute the values into the formula to find the volume:
V = π*(8 feet)^2 * 4.17 feet
V ≈ 3.14 * 64 square feet * 4.17 feet
V ≈ 839.64 cubic feet
Therefore, the volume of the pool once filled to 5/6 of the way is approximately 839.64 cubic feet.
To find the volume of the pool, we will need to use the formula for the volume of a cylinder, since a pool is typically cylindrical in shape. The formula for the volume of a cylinder is V = π * r^2 * h, where V is the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the pool, and h is the height or depth of the pool.
Given that the pool has a depth of 5 feet and a radius of 8 feet, we can substitute these values into the formula:
V = π * (8^2) * 5
To calculate the volume, we first need to square the radius: 8^2 = 64.
Now, we can calculate the volume:
V = π * 64 * 5
Since we're asked to fill the pool only 5/6 of the way, we need to find 5/6 of the calculated volume:
V_filled = (5/6) * V
Substituting the value of V, we get:
V_filled = (5/6) * (π * 64 * 5)
Now we can simplify the equation by multiplying:
V_filled = (5/6) * (3.14159 * 64 * 5)
Calculating further:
V_filled = (5/6) * (3.14159 * 320)
V_filled ≈ 837.758442333... cubic feet
So, once the pool is filled up to 5/6 of its depth, the volume of the pool will be approximately 837.76 cubic feet.