Differential Calculas?

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Differential Calculas?

Q. Find the volume of solid generated by the revolution of upper half of parabola y2 = 4ax about the x axis.

2007-05-30 21:01:52 · 3 answers · asked by shitanshu s 1 in Science & Mathematics ➔ Mathematics

3 answers

Volume of revolution is V = ∫πy²dx between limits

V = ∫π4axdx between 0 and some value x = t

= π4a[x²/2] between 0 and t

= 4πa (t²/2 - 0)

= 2πat²

The volume as you have specified it is infinite.

2007-05-30 23:48:58 · answer #1 · answered by fred 5 · 0⤊ 1⤋

dy/dx = 4a/2y

2007-05-31 04:08:59 · answer #2 · answered by misshahila 2 · 0⤊ 1⤋

y = 2âax
. . . . . . . . x
V = 4Ïâaâ«âx dx
. . . . . . . 0

V = (8Ï/3)â(ax^3)

2007-05-31 04:17:50 · answer #3 · answered by Helmut 7 · 0⤊ 1⤋