Todd has a new spool of wire. he needs 48 pieces of wire, each 22 feet long. he estimates that he needs 50×20=1000 feet, and he concludes that 1 spool with 1000 feet will be enough. should todd use multiplication to estimate the total amount of wire he needs? explain your reasoning.

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Step-by-step explanation:

Todd has a new spool of wire. He needs 48 pieces of wire, each 22 feet long. He estimates that he needs 50×20=1000 feet, and he concludes that 1 spool with 1000 feet will be enough.

Actually, Todd is incorrect because in his estimation he took 2 more pieces than he needed of the length 2 feet shorter that he needed. The total length may appear smaller. Check this:

So, Todd shouldn't use multiplication 50×20=1000 to estimate the total amount of wire he needs.

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.

d

step-by-step explanation: