Your hole punch makes holes in your that have diameter of 4^-1 inch.

a.Write an expression for the area of one punched hole. Use the formula for the area
of a circle A=:r^2.
(: is pi sign)

b.Your hole punch makes three holes in a page . Write an expression for the total
area punched out of one sheet of paper.

a). 4^(-1) is the same as 1/4. Since this is the diameter, you divided it by the 2 to get the radius. So the radius is 1/8. Now the expression is:

A= pi*(1/8)^2 or A=(1/64)*pi
b). In part a, the expression is for the area of one punched hole. Since you have three punched holes now, you multiply the expression in part A by 3. So now the expression is: A=3pi*(1/8)^2 or A=(3/64)*pi

Thank you it help a lot

a. The expression for the area of one punched hole can be written as A = π(4^-1/2)^2.

b. To find the total area punched out of one sheet of paper, we need to multiply the area of one punched hole by the number of holes made. So the expression can be written as Total Area = 3 * π(4^-1/2)^2.

a. To find the expression for the area of one punched hole, we can use the formula for the area of a circle, which is A = πr^2. In this case, the diameter of the hole is given as 4^-1 inches, which means the radius (r) is half of the diameter. So, the radius can be calculated as (4^-1) / 2.

The expression for the area of one punched hole can be written as:
A = π * ((4^-1) / 2)^2

b. Since the hole punch makes three holes in a page, we need to calculate the total area punched out of one sheet of paper. To do this, we can multiply the area of one punched hole by the number of holes (which is 3 in this case).

The expression for the total area punched out of one sheet of paper can be written as:
Total Area = 3 * π * ((4^-1) / 2)^2