Question

Find the volume of the solid generated by revolving about the y-axis the region bounded by the given equationsx= y3/2, x=0, and y=9

Answer 1

volume of the required generated cylinder will be = 5153

Explanation:

to calculate volume of solid generation

given
`x = y^{(3)/(2)}`

Volume of solid generated

=
`=\int_(a)^(b)\pi x^2dy\\=\int_(0)^(9)\pi (y^(3/2))^2dy\\=\int_(0)^(9)\pi y^3 dy\\=\pi\int_(0)^(9)y^3 dy\\= \pi [(y^4)/(4)]^9_0\\=5153`

hence, the volume of the required generated cylinder will be = 5153