Volumes! (1 Viewer)

[ashokkumar]

The base of a particular solid is x^2 + y^2 = 4. Find the volume of the solid if every cross-section perpendicular to the x-axis is a parabolic segment with axis of symmetry passing through the x-axis and height the length of its base. (answer = 256/9)

 

[jet]

 

[sifANDREW]

SO GLAD I WAS ABLE TO DO THIS!

this is how i done it

eqn of circle : x^2 + y^2 = 4

with P(x,y) , Q(x,-y)

area of parabola with base 2y and height 2y ( using simpson's area rule)
h = y
y0=0
y1=2y
y2=0
A= y/3(8y)

DeltaArea = (8y^2)/3 Deltax
= 8/3 (4-x^2) deltax

Area = integration from -2 to 2 of 8/3 . (4-x^2)dx
(skipped lim etc because i dont know how to do limit signs =[)

= 16/3 (8 - 8/3) [even function]
= 256/9

hope it helps.

PS. what program did you use to write the equations? i want to type up questions for notes but i dont know how to do the eqns symbols etc lol thanks

 

[Lolsmith]

LaTeX, it is above the quick reply box.

 

[Carrotsticks]

how do you type up normal text in latex without having a ~ symbol after every word?

 

[jet]

\text{insert text here}

The code I used for this solution was too large for the latex editor so I typeset it on my computer and uploaded the image.