2/24/2014
THE AREA OF A FRUSTUM
Theareaofthefrustumofaconeisgivenby
2
Section 8.2
2
⋅ℓ
2
averageradius ⋅ length
Area of a Surface of Revolution
FINDING THE SURFACE AREA
OF A SOLID OF REVOLUTION
• Dividetheinterval ,
subintervals.
into equal
REVOLUTION ABOUT
THE x-AXIS
Letf bepositiveandhaveacontinuousderivative.The
surfacearea ofthesurfaceobtainedbyrotatingthe
curve
,
, aboutthe ‐axis is
• Findtheareaoftheconicalfrustums
createdbyeachsubinterval.
2
∗
∗
1
Δ
• Sumtheareasandtakelimitasthelength
ofthesubintervalsgotozero.Compute
definiteintegral.
2
1
2
1
Ifthecurveis
,
2
NOTE:Forbothcases,
,then
1
2
S =∫2π y ds
REVOLUTION ABOUT
THE y-AXIS
Forrotationaboutthe ‐axis,thesurfacearea
formulais
2 where
1
1
1