How many square inches in a 4.25 inch circle?

Answer 1

A circle that is 4.25 inches implies that its circumference is 4.25 inches; that is, it is 4.25 inches around. The formula for the circumference of a circle is given as c = 2πr, where c is the circumference, pi is a constant (approximately 3.14), and r is the radius of the circle. Since the c-value is known we can use algebra to manipulate the formula in order to solve for r (the only missing piece of information). Doing so yields r = c/2π. Substituting the circumference of 4.25 inches into the formula reveals that the radius must be .68 inches (rounded to two decimal places). Now that the radius of the circle is known, the surface area can be calculated with the formula A = πr2. Substituting the determined value of the radius in for r produces a surface area of 1.45 inches2. The unit of square inches comes from the fact that we are not only multiplying the numerical value of the radius, but also its units. In this case, r2 = (0.68 inches)(0.68 inches) = 1.45 inches2.