Question

Consider the solid obtained by rotating the region bounded by the given curves about the line y = 5.
y = 5x , y = 5 * squareroot of x
Find volume.

Answer 1

considered....now what?

Answer 2

find volume

Answer 3

is it solid of revolution problem in calc

Answer 4

you dont say..... ;)

Answer 5

yup

Answer 6

Ok, we first have to find intersections

Answer 7

have you guys ever heard of the disk or washer method to finding volume?

Answer 8

Yes

Answer 9

and a shell

Answer 10

first things first; whats our boundaries for integration

Answer 11

http://www4d.wolframalpha.com/Calculate/MSP/MSP46219fbd79927442221000038ec20h29g0g1b81?MSPStoreType=image/gif&s=25&w=399&h=188&cdf=Coordinates&cdf=Tooltips

Answer 12

thank you for that link :)
how do you find the boundaries though?

Answer 13

We look the the intersection point which are (1,5)(0,0)

Answer 14

so would the bounaries be from 0 to 5?

Answer 15

yes

Answer 16

So what method would you use?

Answer 17

the y=5 line seems spurious

Answer 18

hmm, im not sure which method to choose

Answer 19

because im looking through my notes right now, it looks like we could use the disk method

Answer 20

Since you are going to be rotating around an horizontal point(y=5) you are going to use disk method( or washer)

Answer 21

in Some cases you can use either but it is matter convienience

Answer 22

the disk method is adding up all the areas of the circles;

[S] 2pi [f(x)]^2 dx - [S] 2pi [g(x)]^2 dx

Answer 23

ohhh....rotating AROUND y=5; haha :) helps to read the question lol

Answer 24

I would advise against blindly memorizing the formula

Answer 25

i have in my notes that the disk method formula is pi (R(x))^2 dx

Answer 26

the formula is jsut the qnqlytic representation of what you are actually accomplishing;

Answer 27

R(x) - 5 in this case

Answer 28

analytic...

Answer 29

So the bigger circle have radius of 5-5x
the smaller circle have radius of 5-5Sqrt[x]

Answer 30

i was combining the shell and the disk ....my mistake

Answer 31

ohh i think i get it. so would it be (5-5sqrt)^2-(5-5x)^2 dx

Answer 32

you simply find the volume of the outer function and cut out the volume of the inner function

Answer 33

I think you have it reversed

Answer 34

[5x-5] ^2 - [5sqrt(x)-5]^2

Answer 35

how come its that way rather than the way i put it? i remember my professor i think tellung us that its the bottom function subtracted from the top one, and in this case, the top function is the 5sqrt of x

Answer 36

i might be confusing it with something else x_X

Answer 37

sine y = 5; you want to bring the function down to y = 0 therefore:

f(x) - 5

Answer 38

since y = 5...yadayada

Answer 39

at y=5; the function is out of reach up on a shelf; you want to get it down to where you can work with it on the table.... bring it down to y=0 by subtracting 5 from it

Answer 40

ohhh, i see what you mean now

Answer 41

thank you guys so much for all the help but im running late for class haha so ill try to work this with what you guys helped me with so far. thank you guys times infinityy !

Answer 42

youre welcome :)