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.

Answer 1

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.