A cylindrical tank is being constructed to hold 10,000 ft^3 of water. The diameter of the tank is 36ft. What is the minimum height needed for the tank?
Vol = π r^2 h
solve for h
10000 = π(18^2) h
To find the minimum height needed for the tank, we can use the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height of the cylinder.
Given that the diameter of the tank is 36 ft, we can calculate the radius (r) by dividing the diameter by 2:
r = 36 ft / 2 = 18 ft
We also know that the volume of the tank should be 10,000 ft^3.
Substituting these values into the formula, we have:
10,000 ft^3 = π(18 ft)^2h
To find the minimum height (h), we can rearrange the equation:
h = 10,000 ft^3 / (π(18 ft)^2)
Calculating the value, we have:
h ≈ 10,000 ft^3 / (π(18 ft)^2)
≈ 10,000 ft^3 / (π(324 ft^2))
≈ 10,000 ft^3 / (1017.88 ft^2)
≈ 9.81 ft
Therefore, the minimum height needed for the tank is approximately 9.81 ft.
To find the minimum height needed for the tank, we first need to find the volume of a cylindrical tank. The volume of a cylinder is calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
Given that the diameter of the tank is 36 feet, we can find the radius by dividing the diameter by 2.
Radius (r) = Diameter / 2 = 36 ft / 2 = 18 ft.
Now, we have the radius of the tank, and we can use the given volume to find the height.
V = πr^2h
10,000 ft^3 = π(18 ft)^2h
Simplifying further:
10,000 ft^3 = π(324 ft^2)h
Dividing both sides by π(324 ft^2), we get:
10,000 ft^3 / (π(324 ft^2)) = h
Using a calculator to evaluate the left side of the equation, we find:
h ≈ 9.68 ft.
Therefore, the minimum height needed for the tank is approximately 9.68 feet.