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Find the volume of the solid generated when R (shaded region) is revolved about the given line.28-- Vx , y = 14, xy14196; about y= 14200The volume of the solid obtained by revolving the region about y 14 is(Type an exact answer, usingT as needed.)

Question
Find the volume of the solid generated when R (shaded region) is revolved about the given line.
28-
- Vx , y = 14, x
y14
196; about y= 14
200
The volume of the solid obtained by revolving the region about y 14 is
(Type an exact answer, using
T as needed.)
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Find the volume of the solid generated when R (shaded region) is revolved about the given line. 28- - Vx , y = 14, x y14 196; about y= 14 200 The volume of the solid obtained by revolving the region about y 14 is (Type an exact answer, using T as needed.)

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Step 1

Consider a shaded disc as shown in the diagram on the white board.

Radius, R = 14 - y; thickness = dx

Volume of this disc = dV = πR2dx

We need to integrate this over over x = 0 to x = 196 to get the entire volume of the solid.

28
y 14
Disc of radius R = 14 - y and
thickness dx
200
X
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28 y 14 Disc of radius R = 14 - y and thickness dx 200 X

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Step 2

Please see the white...

R 14-y14-(14-x)= x
dV =D πR'dv = r(Vx)'dx = rxdr
196
x-196
V =
dV = | Txdr = "[x2]96 - 192087
2
x=0
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R 14-y14-(14-x)= x dV =D πR'dv = r(Vx)'dx = rxdr 196 x-196 V = dV = | Txdr = "[x2]96 - 192087 2 x=0

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Math

Calculus

Integration

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