finding volume of a solid using cross sectional areas
TRANSCRIPT
Finding Volume of a solid using cross-sectional areas
Stephanie Yang G11 AP-Calculus
Find the volume of a solid with given base and cross-sections.
,x-16y:Base 2
. triangleslequilatera are
axis- x thelar toperpendicu sectionsCross ]4,4[
,16y:Base 2x
. triangleslequilatera are
axis- x thelar toperpendicu sectionsCross ]4,4[
-4
44
,16y:Base 2x
. triangleslequilatera are
axis- x thelar toperpendicu sectionsCross ]4,4[
)16,( 2xx
)0,(x
2
22
222
16
)16(
)()016(
x
x
xxxs
s
Distance formula to find the
length of a side
,16y:Base 2x
. triangleslequilatera are
axis- x thelar toperpendicu sectionsCross ]4,4[
216 xs
)16,( 2xx
)0,(x
s
s
2
4
3
trianglelequilateraan of Area
s
2
222
4
334
)16(4
3)16(
4
3 section -crosseach of Area
x
xx
,16y:Base 2x
. triangleslequilatera are
axis- x thelar toperpendicu sectionsCross ]4,4[
)16,( 2xx
)0,(x
s4
4
324
4 12
334)
4
334(
xxdxxV
3
364
3
3)3296(
3
332332
3
316316
3
316316
))4(12
3)4(34()4(
12
3)4(34 33
The volume of the solid formed is .3
364