The volume of the solid of revolution is [tex]\frac{7\pi}{3}[/tex] cubic units.
How to find the volume of a solid of revolution with respect to an axis parallel to a Cartesian axis
The statement has been represented in the image attached below, the formula for the solid of revolution is presented below:
[tex]V = \pi \int\limits^{1}_{0} {[5\cdot y^{2}-2]^{2}} \, dy[/tex] (1)
[tex]V = \pi \int\limits^{1}_{0} {(25\cdot y^{4}-20\cdot y +4)} \, dy[/tex]
[tex]V = 25\pi\int\limits^1_0 {y^{4}} \, dy -20\pi\int\limits^1_0 {y^{2}} \, dy +4\pi\int\limits^1_0\, dy[/tex]
[tex]V = \frac{7\pi}{3}[/tex]
The volume of the solid of revolution is [tex]\frac{7\pi}{3}[/tex] cubic units. [tex]\blacksquare[/tex]
To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504
