The Giant Ocean Tank in Boston's New England Aquarium is a cylinder that is 23 feet high and has a volume of 200,000 gallons, (1 gallon = 0.134 ft^3). Find the diameter of the tank.
V=200,000gal * 0.134Ft^3/gal=26800Ft^3.
V = pi*r^2 * h = 26,800 Ft^3.
3.14r^2 * 23 = 26800.
72.22r^2 = 26800.
r^2 = 371.1.
r = 19.26 Ft.
D = 2r = 2 * 19.26 = 38.5 Ft.
To find the diameter of the tank, we can use the formula for the volume of a cylinder, which is given by:
V = π * r^2 * h
Where:
V = volume of the cylinder
π = Pi, approximately 3.14159
r = radius of the cylinder's base
h = height of the cylinder
First, let's convert the volume from gallons to cubic feet. Since 1 gallon is equal to 0.134 cubic feet, we can multiply the volume by the conversion factor:
Volume in cubic feet = 200,000 gallons * 0.134 ft^3/gallon
Next, let's rearrange the formula for the volume to solve for the radius (r):
r = √(V / (π * h))
Now we can substitute the given values into the equation:
r = √(200,000 * 0.134 / (π * 23))
Using a calculator, we can evaluate the expression inside the square root and calculate the radius. Then, to find the diameter (d) of the tank, we multiply the radius by 2:
d = 2 * r
Calculating the expression and performing the final calculation will give us the diameter of the tank.