Question

I've been studying geometry from 11am-10pm(now) and the result I got isn't the one it should be....Please help me!!! PLEASE ^_^
In the triangle ABC AB=8 and BC=12,the angle between AB and BC is 60 degrees.The triangle rotates around BC.Find the volume of the 'thing' formed from this rotation :)

Answer 1

rotates around bc? really

Answer 2

O.o yes it does...I can draw a pic if u want....

Answer 3

k here i will tell u how to do it
when u rotate a triangle about 1 of its sides u get a figure with two cones of same radius attached now try to find the hight of each cone and u have the radius which is hight of the triange from side BC so u will have the volume by the formula V of cone = (1/3)(pi)(r^2)h

Answer 4

like in a circle?

Answer 5

yea i know that thnx :)
but the problem is that i am not sure...we can't count the area of the circle formed twice can we?

Answer 6

its not gonna count twice

Answer 7

so it must be V=V1+V2-piR^2?

Answer 8

or not?

Answer 9

volume top cone + volume bottom cone = volume of rotation

Answer 10

amistre is correct

Answer 11

when you press your hands together; do you subtract the volume created by them touching?

Answer 12

you add the volume of one to the other;

Answer 13

how abt the circle? O.o

Answer 14

a circle has a area not a volume

Answer 15

the circle is just a way to measure the volume for the top and the volume for the bottom

Answer 16

yea but it will be counted twice since the same cones have the same base right?

Answer 17

when....bases..touch.... they dont count as ....twice anything

Answer 18

when you press your hands together; no EXTRA volume is created to take away

Answer 19

when you stack a can of corn on top of another can of corn; you havent add any EXTRA volume by staking

Answer 20

the place where they touch, is just that .... the place where they touch

Answer 21

prolly what your thinking of is that you are used to seeing area as a surface that has some depth to it; when area is infinitely thin has zero depth

Answer 22

How the hell do you form 2 cones by rotating about one of the edges? The tip of the triangle (point A) will make a circle through space...

Answer 23

an edge make an axel in space

Answer 24

ever play with those claker balls on a stick?

Answer 25

Right, so all points on edges AB, an AC will form circles when rotated all the way about the BC axis

Answer 26

right

Answer 27

oooh, ok i was thinking about it wrong, i was thinking 2 cones with their tips being point A

Answer 28

why is there 2 cones?

Answer 29

ABC, AB = 8, BC = 12
< ABC = 60

Answer 30

becasue the triangle is spun on an edge makind a top and bottom cone

Answer 31

The circle that A makes through space is the base of both cones, One cone is formed by each half of the triangle rotating 360 degrees through space

Answer 32

i get a radius of 7; and a height of 4 for the top

i get a radius of 7 and a height of 8 for the bottom part

Answer 33

you mean a right and left cone, not top and bottom

Answer 34

does it really matter how we hold the edge?

Answer 35

lol

Answer 36

(1/3) pi 49(4) + (1/3) pi 49(8) should be the volume round abt

Answer 37

615.75.... is the best I can do with truncating numbers

Answer 38

i dont follow the rotation, also your triangle doesnt make sense, can you label things

Answer 39

one sec

Answer 40

ok i drew my triangle a little differently , so first maybe its smarter to actually find the other angles and sides, so we dont just guess the shape

Answer 41

mines not to scale :)

Answer 42

Think about a flag, that is a right triangle. rotate that flag around the flag pole. You get one cone.

The triangle we are dealing with is not a right triangle but can be divided in half and considered as 2 right triangles. So 2 cones.

Answer 43

so i get 8 sin 60 for the radius , 8 sin pi/3

Answer 44

8 sin pi/3 ~ 6.92

Answer 45

if we want accuracy; it should go

\[\frac{pi (8sin(30))^2*4}{3}+\frac{pi (8sin(30))^2*8}{3}\]

Answer 46

how do you get 4

Answer 47

oh 8 sin pi/6

Answer 48

lol.... i did sin instead of cos :)

Answer 49

8sin(30) = height of top = 4

Answer 50

12 - 4 = 8 for height of bottom

Answer 51

ok , so change sin to cos in your formula

Answer 52

yes ...

Answer 53

ok looks good !

Answer 54

we can clean it up by factoring:

\[\frac{4\pi (8cos(30))^2}{3}(1+2)\] right?

Answer 55

16 /3 pi ( 8 cos (pi/6))^2

Answer 56

woops

Answer 57

\[4\pi\ (8 cos(30))^2\]
seems to be the simplest form

Answer 58

4/3 pi ( 8 cos ( pi/6))^2

Answer 59

grrr

Answer 60

:) 603.185.....

Answer 61

this interface is not forgiving

Answer 62

can i ask a quick question, given a focus and directrix, there is only one e such that e = 1 , so there is only one parabola

Answer 63

we dint use eccentricity much, so Id have to look it up; but libraries closing so I gotta move to the veranda :)

Answer 64

but there are many ellipses and parabolas

Answer 65

ok bbl ?

Answer 66

:(:(:(:(I'm sooooo sorry guys..:(:( chrome wasn't responding :(:(I'm sorry :(

Answer 67

Hmmmm......the V=192pi tht's wht the answer must be acc.to my math book

Answer 68

Thanks for trying anyway :) ^_^