Thread: Due tomorrow, calculus question invlolving circumference and diameter

The diameter of a tree was 25 cm. During the following year the
circumference increased by 5 cm.

Using calculus, find

(a)

how much the tree’s diameter has changed ?

(b) what is the corresponding change in the tree’s cross-section area ?

I just dont know what to do.

The two equations you need are:
2*pi*radius = circumference
pi *(radius)^2

radius is half the diameter
so before the increase in circumference occured, the circumference was

2*pi*25 cm = 50 * pi cm

increasing this by 5 cm gives us

new circumference = 50*pi + 5

using this to find the radius

50*pi + 5 = 2*pi*radius
solving for the radius by dividing both sides of teh equation by 2*pi gives

new radius = (50*pi + 5)/(2*pi)

doubling to give diamter

new diamter = (50*pi +5)/pi

change in diameter = new diamter - old diamter

= (50*pi +5)/pi - 25 cm

new cross section area = (new radius ^2) * pi
old cross section area = (old radius ^2) * pi
difference in cross section area = new cross section - old cross section


That should get you through it, year 7 maths can be tough!!!University gets much worse!!!

is that calculus? because usually it seems to involve dy/dx and stuff like that.

It is still calculus, algebra is calculas lol, ask your teacher or a friend, but I'm pretty certain thats right, there shouldnt be an differentiating

I'm guessing your from Griffith [question is identical to the one we were given and it's due at the same time] , if you are, it gives you a hint at the bottom of the assignment, which is to use the small change formula... Examples of the small change formula are on page 136 of the module 2 lecture note book.


if this helps at all.... you'll want to find a formula that relates to the diameter and circumference, re-arrange if necessary to relate it to what you want to find, which is the diameter, find the derivative of the equation, times the derivative by the change.