Waters fills a spherical tank of diameter 16 meters until the water is 4 meters deep at the lowest point in the tank. What is the diameter of the surface of the water?
To find the diameter of the surface of the water, we can consider the diameter of the tank and the depth of the water.
Given:
Diameter of the tank = 16 meters
Depth of the water = 4 meters
To find the diameter of the surface of the water, we need to subtract twice the depth of the water from the diameter of the tank.
Diameter of the surface of the water = Diameter of the tank - 2 * Depth of the water
Diameter of the surface of the water = 16 meters - 2 * 4 meters
Diameter of the surface of the water = 16 meters - 8 meters
Diameter of the surface of the water = 8 meters
Therefore, the diameter of the surface of the water is 8 meters.
To determine the diameter of the surface of the water, we need to visualize the situation. The tank can be thought of as a sphere, and the water inside it will also take the shape of a sphere, but only partially filled.
First, let's determine the radius of the sphere representing the tank. Since the tank has a diameter of 16 meters, the radius can be calculated by dividing the diameter by 2:
Radius = Diameter / 2 = 16 meters / 2 = 8 meters.
Next, let's determine the radius of the partially filled sphere representing the water. We know that the water is 4 meters deep at the lowest point. When water fills a spherical container, the water level will also form a sphere, with its center being the same as the overall sphere (the tank).
At the lowest point, the water's depth is 4 meters, which means the radius of the water sphere will be equal to the radius of the tank minus the depth of the water:
Water Sphere Radius = Tank Radius - Water Depth = 8 meters - 4 meters = 4 meters.
Now, we can find the diameter of the surface of the water. Since the diameter of a sphere is simply twice its radius, we can calculate the water surface diameter as:
Water Surface Diameter = 2 * Water Sphere Radius = 2 * 4 meters = 8 meters.
Therefore, the diameter of the surface of the water in the tank is 8 meters.