Question

A spherical fish bowl has diameter 26 cm.
The surface of the water in the bowl is a
circle with diameter 20 cm.
a) What is the maximum depth of the water?
b) How many different answers are there for part a? Explain.

Answer 1

Draw it !
radius up high = 20/2 = 10
radius at center where depth is 13 = 13
right triangle radius 10, hypotenuse 13 so water level above center = y
y^2 + 10 ^2 = 13^2
y^2 = 169 - 100 = 69
y = 8.3
so total depth = 13 + 8.3 = 21.3

There is also a line that wide 8.3 below center BUT they asked for the MAXIMUM