1988 Hsc (1 Viewer)

[Mc_Meaney]

I have a question from the 1988 HSC (lol) that I need help with.

The region bounded by the curve y=x^.5 -1, lines x=2, x=3 and the x=axis is rotatated bout the x-axis. Find the folume of revolution so formed.

Ithink the anser is 0.36 but i have no idea :S

:mad1: Help:mad1:

 

[Riviet]

Volume =
3
π∫(x^1/2 - 1)² dx=
2

3
π∫x-2x^1/2+1 dx
2

Unfortunately, the numbers aren't nice, so you'll have surds and fractions to deal with. Don't give decimal approximations unless asked to do so in the question and leave your answer in terms of π.

 

[Mc_Meaney]

Thanks buddy, I can always count on you to make me feel like a puny mathematical mind

 

[Mc_Meaney]

Lol. dont suppose you want to do it again though?

I've just started Trig Functions and am doin arc length atm.

I seem to be goin alright up until this question

"Radius is 7.2mm and angle subtended 55 degrees"

All the q's ive don e so far have it in like pi format already...help?

 

[Riviet]

Convert degrees into radians and vice versa like this:

1 degree = 1 x pi/180 radians, so for 55^o just multiply 55 by pi/180 to convert 55^o to radians.
55 x pi/180 = 11pi/36 radians.

1 radian = 1 x 180/pi degrees, so for converting pi radans to degrees, multiply by 180/pi to get 180^o.

Hope that helps.

 

[Mc_Meaney]

Thanx buddy, owe you another one.

 

[Mc_Meaney]

Volume =
3
π∫(x^1/2 - 1)² dx=
2

3
π∫x-2x^1/2+1 dx
2

Unfortunately, the numbers aren't nice, so you'll have surds and fractions to deal with. Don't give decimal approximations unless asked to do so in the question and leave your answer in terms of π.

I got it down to ---> (1-2x2^1/2+2x3^1/2) π units³

hope that looks good