A plate with an area of 500 square inches is shown. A pizza is inside the plate. The diameter of the pizza is one-half the diameter of the plate.
Let's call the diameter of the plate D.
Therefore, the diameter of the pizza is D/2.
The area of a circle is given by the formula: A = πr^2, where r is the radius.
Since the radius is half the diameter, the area of the pizza is: A_pizza = π(D/4)^2.
Since the area of the pizza is given as 500 square inches, we can set up the equation:
π(D/4)^2 = 500.
Solving for D, we get:
(D/4)^2 = 500/π.
Taking the square root of both sides gives us:
D/4 = √(500/π).
Multiplying both sides by 4 gives us:
D = 4√(500/π).
So, the diameter of the plate is 4 times the square root of 500 divided by π.