Atank on a water tower is a sphere of radius 30 feet. determine the depths of the water when the tank is filled to one-fourth and three-fourths of its total capacity. (note: use the zero or root feature of a graphing utility after evaluating the definite integral. round your answers to two decimal places.)

Part 1) When the tank is 1/4 filled the depth of liquid is 19.581 feet.

Part 2) When the tank is 3/4 filled the depth of liquid is 40.42 feet.

Step-by-step explanation:

The volume of the sphere of radius R when it is filled up to a depth 'h' from the base equals

Case 1) When the tank is 1/4 full we have

Upon equating the values we get

Putting R = 30 feet and solving for 'h' we get

h = 19.581 feet.

Case 2) When the tank is 3/4 full we have

just sum

10 + 10 = 20