Answer to Question #176661 in Calculus for Joshua

Question

Use the method of disks/rings to determine the volume of the solid obtained by rotating the region bounded by y=√x, y=3 and the y-axis about the y-axis.

Answer 1

Here the region is rotating about y-axis as shown below

Volume of the solid obtained by

rotating the region bounded by y=√x, y=3 and the y-axis about the y-axis.

= $\int_{0}^{3} πx²dy$

= $π\int_{0}^{3} x²dy$

= $π\int_{0}^{3} y ^4dy$ since y = √x

= $π[ \frac{y^5}{5}]_{0}^{3}$

= π($\frac{3^5}{5}$ )

= $\frac{243π}{5}$

= 48.6π

So the required volume will be $\frac{243π}{5}$ cubic unit = 48.6π cubic unit