Problem:
A large sphere is on a horizontal field on a sunny day. At a certain time the shadow of the sphere reaches out a distance of m from the point where the sphere touches the ground. At the same instant a meter stick (held vertically with one end on the ground) casts a shadow of length m. What is the radius of the sphere in meters?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
We first construct the figure shown, which results from bisecting the sphere-shadow configuration with a vertical plane. Since the meter stick casts a shadow of and hence . Now is similar to .
Thus or .
So or .
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