Answered

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Sixteen times the reciprocal of the number of inches in the circumference of a circle equals the number of inches in the diameter of the circle. What is the number of square inches in the area of the circle

Sagot :

sqdancefan

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

__

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.

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