The volume of the solid obtained by rotating about x-axis by using cylindrical shell method is
`V = int_a^b 2piyf(y) dy`
The given information is
The curves
`y = x^3 =gt x = y^(1/3) `
`y = 8` , `x = y = 0` and rotation is about y-axis
`therefore V = int_0^8 2piy[y^(1/3) - 0] dy `
=`2pi int_0^8 y^(4/3) dy `
...
The volume of the solid obtained by rotating about x-axis by using cylindrical shell method is
`V = int_a^b 2piyf(y) dy`
The given information is
The curves
`y = x^3 =gt x = y^(1/3) `
`y = 8` , `x = y = 0` and rotation is about y-axis
`therefore V = int_0^8 2piy[y^(1/3) - 0] dy `
=`2pi int_0^8 y^(4/3) dy `
= `2pi 3/7 y^(7/3)|_0^8 `
= `(6pi)/7 * 8^(7/3)`
= `(6pi)/7 * 2^7`
= `(768pi)/7`
`therefore` The required volume is `(768pi)/7`
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