# Erica has 8 squares of felt, each with area 16. For a certain craft project she cuts the largest circle possible from each square felt. What is the combined area of the excess felt left over after cutting out all the circles?

A) 4(4-pi)

B) 8(4-pi)

C) 8(pi-2)

D) 32(4-pi)

E) 16(16-pi)

## So each square has an area of 16 units^2, so each side is 4 units.

the circle on each square will have a radius of 2 units, for an area of π(2^2) or 4π

so the left over from each square is 16 - 4π units

or 4(4 - π)

Now, how many squares did you have ?

## Okay.. I worked on The problem a little more, but I got D.

Because the area of the squares would be 32(4)

The area of the circles is 32pi

So then wouldn’t the answer be 32(4-pi)

## To find the combined area of the excess felt left over after cutting out all the circles, we first need to find the area of the circles, and then subtract it from the total area of the squares.

Each square has an area of 16, so the side length of each square is √16 = 4.

The largest possible circle that can be cut out from each square is a circle whose diameter is equal to the side length of the square, which is 4. So, the radius of each circle is 4/2 = 2.

The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Therefore, the area of each circle is A = π * 2^2 = 4π.

Since Erica has 8 squares, she will have 8 circles to cut out.

The combined area of the circles would be 8 * 4π = 32π.

The total area of the squares is 8 * 16 = 128.

To find the combined area of the excess felt left over, we subtract the area of the circles from the total area of the squares: 128 - 32π.

Simplifying the expression, we get: 128 - 32π.

Therefore, the combined area of the excess felt left over after cutting out all the circles is 128 - 32π.

So, the correct answer is D) 32(4-pi).

## To solve this problem, we need to find the combined area of the excess felt left over after cutting out the circles.

We are given that Erica has 8 squares of felt and each square has an area of 16. So, the total area of all the squares combined is 8 * 16 = 128.

To find the area of the excess felt, we need to subtract the sum of the areas of all the circles cut out from the squares from the total area of the squares.

Now, let's find the radius of the largest circle that can be cut out from each square. The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.

Since the area of each square is 16, we can equate the area of the square to the area of the circle and solve for the radius:

16 = πr^2

Dividing both sides by π gives us:

r^2 = 16/π

Taking the square root of both sides gives us:

r = sqrt(16/π)

Now, we can find the area of each circle using the radius:

A = π * (sqrt(16/π))^2 = π * (16/π) = 16

So, the combined area of all the circles is 8 * 16 = 128.

Finally, to find the area of the excess felt, we subtract the sum of the areas of the circles from the total area of the squares:

Excess area = Total area of squares - Sum of areas of circles = 128 - 128 = 0.

Therefore, the correct option is:

D) 32(4-pi)

Because the area of the excess felt left over after cutting out all the circles is 0.