Question 1184074: The resistance, R, of a wire varies directly as its length and inversely as the square of its diameter. If the resistance of a wire 4000ft long with a diameter of 0.18 inches is 7867 ohms, what is the resistance of 4300ft of the same type of wire with a diameter of 0.27 inches? (Leave k in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredth.)
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a reference.
https://www.purplemath.com/modules/variatn.htm
this problem is in the reference.
it's on the third page i believe.
it's good for you to read each page though, as it contains good information on how to solve the different variation formulas.
in your problem, the formula is R = k * L / d^2
R is the resistance
L is the length of the wire.
d is the diameter of the wire.
k is the constant of variation.
when L = 4000 feet and d = .18 inches, R = 7867 ohms.
R = k * L / d^2 becomes:
7867 = k * 4000 / .18^2
solve for k to get:
k = 7867 * .18^2 / 4000 = .0637227.
k, being the constant of variation, will stay the same and will be used to solve the question.
the question is:
what is the resistance of 4300 feet of the same type of wire with a diameter of .27 inches.
R = k * L / d^2 becomes:
R = .0637227 * 4300 / .27^2.
solve for R to get:
R = 3758.677778.
round to the nearest hundredth to get:
R = 3758.68.
that's your answer.
the link to each page in the reference is on the bottom of each page of the reference.
if you want to go directly to the third page, then click on https://www.purplemath.com/modules/variatn3.htm
but then, you'll miss all the good stuff on pages 1 and 2.
Answer by greenestamps(13203)  (Show Source):
You can put this solution on YOUR website!
The post implies that we are supposed to find the constant of variation k; but there is no need to do so.
Changing the length from 4000ft to 4300ft increases the resistance by a factor of 4300/4000 = 43/40.
Changing the diameter from 0.18 inches to 0.27 inches decreases the resistance by a factor of (.27/.18)^2 = (3/2)^2 = 9/4.
ANSWER: 7867*(43/40)/(9/4) = 7867*(43/40)*(4/9) = 3758.677777... = 3758.68 to the nearest hundredth.
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