Question

To make circular cake boards, a company cuts circles out of plastic squares. The circles are cut as wide as the squares to lessen the amount of wasted material. Use the drop-down menus below to complete statements about the amount of wasted material for circular cake boards with a diameter of d.
The area of the wasted material is given by the difference:____-______
d^2
4d
π(d/2)^2

Answer 1

Answer:

d^2 - π(d/2)^2

Step-by-step explanation:

Since the diameter of the circle is equal to the side of a square (d), that means that we have a circle inscribed in square.

If we draw a square and inscribe a circle in it, all parts of the square outside the circle will be waste, in this particular case.

If we want to find the area of the wasted material we need to subtract the area of the circle from the area of the square.

Area of the circle is:

P1 = πr^2, r being the radius

Since radius is half the diameter, that means that:

P1 = π • (d/2)^2

Area of the square whose side is d is:

P2 = d^2

So, the area of wasted material is:

P = P2 - P1

P = d^2 - π(d/2)^2