Question

calculus problem

Answer 1

the disc has an infinitesimal volume of
dV=area of disc * the infinitesimal height=2*pi*r^2 * dy

total volume is sum (integral) of all such tiny volumes from y=0 to y=9
\[V\pi\int_{y=0}^9r^2dy\]

Answer 2

oooooo yes but then idk how to go from there cuz the bakc of the book says a. 40.5pi or 127 and i got 243..

Answer 3

so, put them there...
\[
V=\pi\int_0^9(\sqrt{9-y})^2dy=\pi\int_0^9(9-y)dy=\pi\left[9y-{y^2\over2}\right]_0^9\\
V=\pi(81-81/2)={81\pi\over2}
\]

Answer 4

what about b.

Answer 5

use simpson's, trapeziodal or Reimann sums or other numerical methods to approximate the value..

Answer 6

"Numerical"....

Answer 7

they should be very close.. Analytical is the most accurate one and numerical ones based on your "h" value (interval size).. the more number, more work to do , more accurate

Answer 8

o ok imma try trapezoidal

Answer 9

whats n again

Answer 10

just choose one.. try 20 pieces?

Answer 11

can u show me ur work? i just got 60.5 -_-

Answer 12

no. put yours.. that way you "learn" :)

Answer 13

btw, is that close to 40.5*pi?

Answer 14

not really cuz im supposed to get arund 30 according to my friend

Answer 15

nope... 40.5*3.14 is a little more than 121

Answer 16

or 127 like you said in your previous reply.

Answer 17

i mean for b.. but ok lol

Answer 18

both are the same volume! gotta be equal

Answer 19

oh ok thank you 1: D