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 result:

V1 =  0 cm3
V2 =  50.2655 cm3

Solution:

a=4 cm v=6 cm f(x)=qx2 f(a/2)=q(a/2)2=v 6=q 22  V1=q=6/22=32=1.5=0 cm3
f(x)=v64x2 f(x)=664x2  x0=a/2=4/2=2 x1=a/2=4/2=2  V2=π x0x1f(x)dx V2=π x0x1(64x2v)dx V2=π [64 x3/3vx]x0x1  F(x)=6x64 x3/3 F1=6 x164 x13/3=6 264 23/3=8 F0=6 x064 x03/3=6 (2)64 (2)3/3=8  V2=π (F1F0)=3.1416 (8(8))=50.2655 cm3



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