A typical house in the 1950's had a concrete rectangular water cistern in their basement to hold water for all the household needs. The inside dimensions were 10 feet 6 inches by 7 feet by 6 feet 6 inches. If 1 cubic foot of water weighs 62 pounds 8 ounces, calculate the weight of the water to the nearest ton if the cistern was completely filled with water.

Sure, let's break this down step by step:

1. First, we need to find the volume of the cistern in cubic feet. The dimensions are given in feet and inches, so we need to convert the inches to feet. There are 12 inches in a foot, so 6 inches is 0.5 feet. Therefore, the dimensions in feet are 10.5 feet by 7 feet by 6.5 feet.

2. The volume of a rectangular prism (which is what this cistern is) is length x width x height. So, we multiply these dimensions together to get the volume: 10.5 feet * 7 feet * 6.5 feet = 474.75 cubic feet.

3. Next, we need to find the weight of the water. We're told that 1 cubic foot of water weighs 62 pounds 8 ounces. First, let's convert the ounces to pounds. There are 16 ounces in a pound, so 8 ounces is 0.5 pounds. Therefore, 1 cubic foot of water weighs 62.5 pounds.

4. To find the total weight of the water, we multiply the volume of the cistern by the weight of 1 cubic foot of water: 474.75 cubic feet * 62.5 pounds/cubic foot = 29,671.875 pounds.

5. Finally, we need to convert this weight to tons. There are 2000 pounds in a ton, so we divide the weight in pounds by 2000 to get the weight in tons: 29,671.875 pounds / 2000 = 14.84 tons.

So, if the cistern was completely filled with water, the water would weigh approximately 15 tons (rounded to the nearest ton).