Is it possible to find an example of a bounded region in the x, y plane that satisfies the following condition : when you revolve the region about the x axis you obtain a solid that has a volume equals its surface area
yes :)
do you want me to cite an example?
please i need an example !
please can you give me an example?
please can you give me an example?
sorry i haven't replied to your reply earlier. anyway, here's an example:
there are many possible examples for this. but since we need to calculate volume (V) and surface area (SA), we choose a figure where its V and SA can easily/readily be calculated.
for instance we want to generate a shape of a cylinder,, note that this only requires a line parallel to x-axis (but not passing through x-axis) so that if it's revolved about the x-axis, it becomes a cylinder, or y = c, where c = any real number except zero. now we only need to find the bounds. for simplicity, let's choose one of the bounds as the origin.
recall that the V and SA of a cylinder is given by
V = π(r^2)*h
SA = 2πrh + 2πr^2
where r is radius and h = height
then we choose a value for V and SA . let's choose, for instance, 100 :
V = 100 = π(r^2)*h
SA = 100 = 2πrh + 2πr^2
since there are two equations, two unknowns, by substitution, we get two pairs of answers:
(i) r = 2.218 ; h = 20.327
(ii) r = 5.696 ; h = 3.08219
here, let's just choose (i).
when the equation y = c is revolved, the cylinder generated has a symmetry on x-axis (like it's lying/rolling on the floor). thus the radius is the y-coordinate and height is the x-coordinate. therefore y = c becomes
y = r = 2.218
with bounds from origin (0,0) to its height (20.327, 0)
hope this helps~ :)
thank you alot for your help I was really worried because i have to submit the answer tomorrow and i could not do any thing without your help
thank you again
you're welcome~ :)
by the way, i just want to make a correction. fro the value of V and SA, it's not 100, it should be 100*pi = 314.16 . sorry i forgot the pi, because i cancelled it right away, but the answers for r and h is still the same. i'll just retype the correction:
...then we choose a value for V and SA . let's choose, for instance, 100*pi :
V = 100*pi = π(r^2)*h
SA = 100*pi = 2πrh + 2πr^2
...and the rest are correct.
so, the value of V and SA for the dimensions (i) and (ii) we got is equal to 100*pi or 314.16, not 100. sorry~ :P
thenk you jai and sara
in which section you are sara?
sectin 20 what about you?
section 70
nice to meet you
if you need any help just tell me
from wich college you are?