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Answer:
4 square inches
Step-by-step explanation:
The relation between diameter and circumference is ...
C = πd
The problem statement tells us of another relation:
16/C = d
Substituting for C using the above equation, we get ...
16/(πd) = d . . . . . substitute for C
16/π = d² . . . . . . . multiply by d
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The area of a circle is given by the formula ...
A = πr²
Using r = d/2, this becomes ...
A = π(d/2)² = (π/4)d²
Using the above relation for d², the area of the circle of interest is ...
A = (π/4)(16/π) = 4
The area of the circle is 4 square inches.