SOLUTION: 1.POPULATION Suppose each person on the planet stood on a piece of ground that was 3 feet by 3 feet. What are the dimensions of the smallest square piece of land that could hold

Question 86889: 1.POPULATION
Suppose each person on the planet stood on a piece of ground that was 3 feet by 3 feet. What are the dimensions of the smallest square piece of land that could hold everyone on the planet? USE SENSIBLE UNITS!

2. A large rubber ball was floating in a lake when the lake froze. The ball was carefully removed without breaking the ice, leaving a hole 3 feet 4 inches across and 8 inches deep. What was the radius of the ball? (Answer to the nearest 0.1 inches).

3. You have 10 barrels of nails. Some of the barrels are full of nails that weigh 1 ounce. The others are full of nails that weigh 1.1 oz. How can you identify which barrels have which kind of nails while using a digital scale only ONE time?

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
1. world population is approx 6.6 billion ... 3 ft by 3 ft is a square yard, so 6.6 billion square yards

1760yd=1mi ... 6,600,000,000/1760/1760=approx 2131sq mi ... this is a square approx 46.2 mi on a side

2. If you picture a circular cross-section of the ball with a diameter going to the center of the bottom of the hole, a triangle formed by the edge of the hole and the ends of the diameter is a right triangle (inscribed in a semicircle).
Using the diameter (which is the hypotenuse) as the base of the triangle, the altitude is the radius of the hole (20 inches).
This altitude divides the hypotenuse such that the altitude is the geometric mean of the segments ... or 8:40::40:x ... so x=200 ... making the diameter 8+200 or 208 and the radius 104

3. Take 1 nail from the first barrel, 2 from the next, 4 from the next, etc.; lastly taking 2^9 (512) nails from the 10th barrel
Weigh the nails and subtract 1023 (2^10-1) from the total
Multiply this number by 10 to avoid problems with the decimal point
Convert the resulting amount into binary (1's and 0's) and the barrels will be ordered starting with the rightmost (least significant) digit
The barrels with the heavier nails will be 1's and the lighter nails will be 0's
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