Refer to the figure and find the volume V generated by rotating the given region about the specified line.

Mathematics

1 answer:

ANEK [815]3 years ago

7 0

Volume generated by the areas R2 + R3 around the line OC
= (1/3) pi 1^2 * 3 = pi sq units

Volume generated by area R2 around OC is found as follows

the equation of the curve can be written as x = y^4 / 81

Integral between limits y = 0 and 3 of the curve is

pi INT x^2 dy = INT pi y^8 / 81^2 dx

= pi [3^9 / 9*81^2]

= pi/3

So the volume generated by R3 about OC = pi - pi/3 = 2pi/3

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