Pond questions

Question

There grows in the middle of a circular pond 10 ft. in diameter a reed which projects 1 ft. out of the water. When it is drawn down it just reaches the edge of the pond. How deep is the water.

Answer 1

I think the best way to answer this question is to visualize it. First, a circular pond with a 10 foot diameter, which would have a radius of 5 feet (d=2r). This means that if the reed is in the middle of the circle, it is 5 feet from the edge. If the reed just touches the edge when you lay it down, then it must be the same length as the radius (5ft). If, when this 5ft tall reed stands straight up, you can only see 1 foot of the reed, then that means 4 feet is covered by the water, making the pond 4 ft deep.