The formula for area is πr²:

a = πr²
a = π(3²)
a = 9π

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

y² - 16y + 43 = -3y + 3
y² - 16y + 43 - 3 = -3y
y² - 16y + 3y + 40 = 0
y² - 13y + 40 = 0

Next, factor the quadratic equation:

y² - 13y + 40 = 0
(y - 5)(y - 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 5) or (y - 8) must equal zero:

If (y - 5) = 0, y must equal 5
If (y - 8) = 0, y must equal 8

So the solution is that y = 5 or 8

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce 6 as well and sum (Inside, Outside) to equal 5. For this problem, those two numbers are 2 and 3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 5y + 6
y² + (2 + 3)y + (2 x 3)
(y + 2)(y + 3)

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).