Apiece of wire x inches long will be bent into the shapes below. write an expression for the enclosed area of a circle in terms of x.

Area of the circle =

Area of square = square inches

Given :

A piece of wire that is x inches long .  It is bent into shape of a circle

Perimeter of circle = x inches

we know that , perimeter of circle =

Now we find area of the circle using the radius

Area of the circle =

Perimeter of square = 4(side)= 4s

4s=x

Divide both sides by 4

Area of square =

Area of square =

Learn more : link

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.