Question

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A company produces circular drink coasters. The equation x2 + y2 = 18.0625, with units in inches, represents the size of a coaster. Each coaster is cut from a square piece of cardboard. What is the minimum possible area of each cardboard piece?

4.25 in^2
8.5 in^2
18.0625 in^2
72.25 in^2

Answer 1

Answer:

D

Step-by-step explanation:

72.25 in^2

Answer 2

The minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².

What is the equation of a circle?

The equation of the circle is the equation that is used to represent the circle in the algebraic equation form with the value of the center point in the coordinate plane and measure of radius.

The standard form of the equation of the circle can be given as,

$(x-h)^2+(y-k)^2=r^2$

Here (h,k) is the center of the circle, and (r) is the radius of the circle.

A company produces circular drink coasters. the equation which represents the size of a coaster is,

$x^2+y^2=18.06$

The units are in inches. This equation can be written as,

$x^2+y^2=(280/16)$

$x^2+y^2=(17/4)^2$

Compare it with the equation of the circle, we get,

h=0

k=0

r=17/4 inch

The radius of the circular coaster is 17/4. Its diameter of it is,

$d=2\times \frac{17}{4}\\ \\d=\frac{17}{2}$

Now, each coaster is cut from a square piece of cardboard. The diameter of the circular coaster will be equal to the side of the square piece of cardboard.

a=d=17/2 inch

The area of the square is the square of its side. Thus, the area of a square piece of cardboard is,

A=a^2

A=(17/2)^2

A=75.25inch^2

Thus, the minimum possible area of each square cardboard piece that is used to produce circular drink coasters is 72.25 in².

Learn more about the equation of circle here;

brainly.com/question/1506955

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