Question

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

Answer 1

4 square inches

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.