Question

can someone explain how much the volume of a cylinder increases when the radius is increased by ten percent

Answer 1

let radius be 100 cm and find its volume

Answer 2

okay

Answer 3

then take radius as 110 and find the volume

Answer 4

but what about the height amount ?

Answer 5

u will get the volume increased

Answer 6

tAKE HEIGHT SAME in both .let it be h

Answer 7

so your saying you want the height to be 110 aswell ?

Answer 8

V = pi (r)^2 h

let r increase by some p%

V' = pi (r(1+p))^2 h

what is the increase?

Answer 9

no height will be same in both cases .i.e. h

Answer 10

V' - V is the amount of increase if im reading it right

Answer 11

amistre i dont get why you put (1+p) in the equation??

Answer 12

because when we increase something by a certain percent: thats the result

Answer 13

r + r(10%) = r(1+10%)

Answer 14

so when say 1 + 10% u mean that the radius ias 10% bigger like in 1.10

Answer 15

correct

Answer 16

*u say

Answer 17

as such:

V' - V

pi r^2 (1.1)^2 h - pi r^2 h

pi r^2 h [(1.1)^2 - 1] would be the increase factor

Answer 18

why did you subtract 1 this time amistre
?

Answer 19

i just pulled out common factors: let a = pi r^2 h

a(1.1)^2 - a = a[1.1^2 - 1]

Answer 20

oh is that suppose to show me that once you take out the whole (100%) ur left with 10%?

Answer 21

let me try this process:

our original volume is: V = pi r^2 h

when we increase r by 10% the new Volume is: V' = pi (r(1.1))^2 h

the amount of increase is the difference between V' and V: V' - V

Answer 22

but i thought that maybe you would be doing the volume + something else because your finding an INCREASE??

Answer 23

oooh nevermind

Answer 24

spose we have something that is 2, and we increase it to get 5

the amount of increase, k is just: 2 + k = 5, or solving for the increase
k = 5-2

Answer 25

your saying to do the volume plus 10% minus the original volmue which will give me 10%

Answer 26

yea i get that

Answer 27

so basically, the volume of the cylinder will increase by ten percent

Answer 28

V = pi (r)^2 h
V' = pi (r(1.1))^2 h

V + k = V'

k = V' - V
k = pi r^2 h (1.1^2 - 1)
k = .21 pi r^2 h

the volume increases by 21%

Answer 29

we can generalize this to any percentage of the radius increase as

the volume increases by [(1+p%)^2 - 1] as the radius increases by p%

Answer 30

im sorry but i dont get how u got .21 . i thought k = the 10% difference but i think im wrong

Answer 31

hmmm, all i did was subtract the old volume from the new volume.

lets compare this to an increase in the radius:

r + k = r'

k = r' - r

k = r(1.1) - r

k = r(1.1 - 1)

k = .1 r , which tells us the the radius increased by 10% as it should of, agreed?

Answer 32

ill be right backk i have to go the bathroom

Answer 33

k

Answer 34

im back.im looking at ur last example

Answer 35

yes.i agree that the radius increased by 10%

Answer 36

the process is the same for volume

V + k = V'

k = V' - V

do you follow how we get to pi r^2 h (1.1^2 - 1) by working the same kind of process?

Answer 37

no because in that example your showing that your multiplying the volumes

Answer 38

i havent multiplied volumes, ive subtracted them ... then simplified it, the same process that I demonstrated with finding the increase in the radius