How to find A for solids of revolution : if cross-section is a disk

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to find A for solids of revolution : if cross-section is a disk if cross-section is a washer 2 2 2 ) ( ) ( ) ( radius inner radius outer A radius A b a b a dy y A V or dx x A V ) ( ) ( me of solids by circular cylinders:

description

Volume of solids by circular cylinders:. How to find A for solids of revolution : if cross-section is a disk if cross-section is a washer. Not solids of revolution:. Volume of solids by cylindrical shells:. Region bounded by y=f(x) 0, y=0, x=a, x=b . Rotation about y -axis. - PowerPoint PPT Presentation

Transcript of How to find A for solids of revolution : if cross-section is a disk

Page 1: How to find  A  for  solids of revolution : if cross-section is a disk

How to find A for solids of revolution:

if cross-section is a disk

if cross-section is a washer22

2

)()(

)(

radiusinnerradiusouterA

radiusA

b

a

b

a

dyyAVordxxAV )()(Volume of solids by circular cylinders:

Page 2: How to find  A  for  solids of revolution : if cross-section is a disk

Not solids of revolution:

Page 3: How to find  A  for  solids of revolution : if cross-section is a disk

Volume of solids by cylindrical shells:

hrrhrrrr

hrhrVVV

2)(2

2 12212

12

212

Region bounded by y=f(x)0, y=0, x=a, x=b. Rotation about y-axis.

dxxfxVb

a

)(2

Page 4: How to find  A  for  solids of revolution : if cross-section is a disk