The graph of a donut is shown below, whose cross-section is a circle with radius r. (1) When
R = 4, r = 2, nd the volume V of the donut. (2) Write down the general expression of the
volume V as a function of R and r.
(1) the equation of the right half of the circle is x = R +
p
r2 ô€€€ y2, while the equation of the
left half of the circle is x = R ô€€€
p
r2 ô€€€ y2.
(2)
R p
r2 ô€€€ x2dx = x
2
p
r2 ô€€€ x2 + r2
2 arctan(p x
r2ô€€€x2 ) + C.
i have uploaded a file of the homework. i missed the classes last week due to illness, so it was very difficult to do the homework. can you please help?
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