esh= 0 and hT 71. A torus (doughnut) Find the volume of the torus formed whenthe circle of radius 2 centered at (3, 0) is revolved about thay-axis. Use geometry to evaluate the integral.ey A-3 21b-is.er,x2U6072. Which is greater? Let R be the region bounded by y = r'and=the

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Asked Sep 2, 2019
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I need help on 71.

es
h= 0 and h
T 71. A torus (doughnut) Find the volume of the torus formed when
the circle of radius 2 centered at (3, 0) is revolved about tha
y-axis. Use geometry to evaluate the integral.
e
y A
-3 21
b-
is.
e
r,
x
2U60
72. Which is greater? Let R be the region bounded by y = r'and
=
the
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es h= 0 and h T 71. A torus (doughnut) Find the volume of the torus formed when the circle of radius 2 centered at (3, 0) is revolved about tha y-axis. Use geometry to evaluate the integral. e y A -3 21 b- is. e r, x 2U60 72. Which is greater? Let R be the region bounded by y = r'and = the

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Expert Answer

Step 1

Equation fo the circle centred at (3, 0) and with radius 2 will be:

(x – 3)2 + (y – 0)2 = 22 = 4

Or, (x – 3)2 + y2 = 4

Please see the white board.

(ax-3)2y
x = 3+
- 1/2
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(ax-3)2y x = 3+ - 1/2

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Step 2

Please see the white board.

T(-rdy
Volume
2
/4- P)
# (3+ /4- 22+(3-\/4-)
-
2
2
dy
6/4- y2 - (9 4- y6/4-y2dy
T[(94
Jo
J4
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T(-rdy Volume 2 /4- P) # (3+ /4- 22+(3-\/4-) - 2 2 dy 6/4- y2 - (9 4- y6/4-y2dy T[(94 Jo J4

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Step 3

Please see the white board.

Now the geometry can be used to evaulate this integral as per any of the two methods below:

Method 1: The area under integral is nothing but the area of the one quarte...

-2
2
12T /4 2dy= 247
V4dy
Volume
V
2
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-2 2 12T /4 2dy= 247 V4dy Volume V 2

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Tagged in

Math

Calculus

Integration