Consider the solid torus (the donut-shaped solid shown in the figure) with radii 7r and 2R. a = 2 b = 7 aR br) (a) Set up an integral for the volume of the given solid. 7r 16-R " V49,2 – y?dy -7r 16т R V49r2 – r?dr -7r 7r 87 R xdr 7r / (49,² – y²)² dy 167 R 7r 87 R ydy -7r (b) By interpreting the integral as an area, find the volume V of the torus. V =

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Chapter2: Second-order Linear Odes
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Consider the solid torus (the donut-shaped solid shown in the figure) with radii 7r and 2R.
a = 2
b = 7
aR
br)
(a) Set up an integral for the volume of the given solid.
7r
16-R "
V49,2 – y?dy
-7r
16т R
V49r2 – r?dr
-7r
7r
87 R
xdr
7r
/ (49,² – y²)² dy
167 R
7r
87 R
ydy
-7r
(b) By interpreting the integral as an area, find the volume V of the torus.
V =
Transcribed Image Text:Consider the solid torus (the donut-shaped solid shown in the figure) with radii 7r and 2R. a = 2 b = 7 aR br) (a) Set up an integral for the volume of the given solid. 7r 16-R " V49,2 – y?dy -7r 16т R V49r2 – r?dr -7r 7r 87 R xdr 7r / (49,² – y²)² dy 167 R 7r 87 R ydy -7r (b) By interpreting the integral as an area, find the volume V of the torus. V =
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