The parabolic segment

The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment

a) around its base
b) around its axis.

Correct answer:

V1 =  51.2 cm3
V2 =  50.2655 cm3

Step-by-step explanation:

a=4 cm v=6 cm f(x) = q x2 f(a/2) = q (a/2)2 = v 6 = q   22  q=6/22=23=1.5  V1=158 v a2=158 6 42=5256 cm3=51.2 cm3
 f(x) = v  46 x2  f(x) = 6  46 x2  x0=a/2=4/2=2 x1=a/2=4/2=2  V2 = π   { x0 }{x1} f(x) dx V2 = π   {x0}{x1} (46 x2   v) dx V2 = π    [46   x3/3  vx]{x0}{x1}  F(x) = 6x  46    x3/3 F1=6 x146 x13/3=6 246 23/3=8 F0=6 x046 x03/3=6 (2)46 (2)3/3=8  V2=π (F1F0)=3.1416 (8(8))=50.2655 cm3



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