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Answer :
When the depth of the water is 8 inches, the radius of the cone is 2.667 inches.
Given that the diameter of the conical figure is 8 inches, while the height of the given conical figure is 12 inches. Therefore, the diagram for the given condition can be made as shown below.
Now, consider the two triangles, ΔABC and ΔAPQ.
The two triangles have a right angle individually and have ∠A in common. Therefore, the two triangles are similar triangles.
Thus, the ratio of the sides can be written as,
AP/AB = PQ/BC
Substitute the values,
8 in/12 in = r / 4 in
r = (8/3) inches
r = 2.667 inches
Hence, the radius is 2.667 inches.
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