Question

If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of the space on the plate that is NOT covered by the napkin

Answer 1

Answer:

Area not covered by napkin = 92.47 sq. in.

Step-by-step explanation:

Complete Question:

A square napkin is folded in half on the diagonal and placed on the diameter of a round plate . If the folded napkin spans the plate and the plate has an 18-inch diameter, what is the area of  the space on the plate that is NOT covered by the napkin?

Solution:

NOT covered area is basically:

Area of Circular Plate - Area of Square Napkin

Area of Circle is given by the formula:

$A=\pi r^2$

Where r is radius, half of diameter (diameter is 18, so radius is 9)

Area of Square = $s^2$

Where s is side length

Diagonal is given as same as diameter, which is 18. We can use pythagorean theorem to find side length of square:

$s^2+s^2=18^2\\2s^2=324\\s^2=162\\s=\sqrt{162}\\s=9\sqrt{2}$

Now, finding the areas:

Area of circle = $\pi r^2 = \pi (9)^2 = 81 \pi$

Area of Square = $s^2=(9\sqrt{2})^2=162$

Area of NOT COVERED AREA = $81\pi - 162 = 92.47$