A spherical water tank holds #6000# #ft^3# of water. What is the diameter of the tank?

To find the diameter of the spherical water tank, you can use the formula for the volume of a sphere, which is given by ( V = \frac{4}{3}\pi r^3 ), where ( V ) is the volume and ( r ) is the radius.

Given that the tank holds 6000 ft(^3) of water, we can set up the equation:

[ 6000 = \frac{4}{3}\pi r^3 ]

To solve for ( r ), first divide both sides by ( \frac{4}{3}\pi ):

[ \frac{6000}{\frac{4}{3}\pi} = r^3 ]

[ r^3 = \frac{4500}{\pi} ]

Then, take the cube root of both sides to find ( r ):

[ r = \sqrt[3]{\frac{4500}{\pi}} ]

Finally, to find the diameter (( d )), multiply the radius by 2:

[ d = 2r = 2 \times \sqrt[3]{\frac{4500}{\pi}} ]

[ d \approx 2 \times \sqrt[3]{\frac{4500}{3.14159}} ]

[ d \approx 2 \times \sqrt[3]{1432.23} ]

[ d \approx 2 \times 11.968 ]

[ d \approx 23.936 ]

So, the diameter of the spherical water tank is approximately 23.936 feet.