Question

Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. Find the volume v of this solid. V =

Answer 1

The solid was obtained by rotating the region bounded by x² = 27y, x = 0, and y = 1 about the y-axis is 42.411 cubic units.

What is integration?

It is the reverse of differentiation.

Consider the solid obtained by rotating the region bounded by the given curves about the y-axis.

$\rm x = 3\sqrt{3y} \ or \ x^2 = 27y$

x = 0, and y = 1

Then the volume of the solid will be

$\rm Volume = \int _{0}^{1} \pi x^2 dy\\\\Volume = \int _{0}^{1} \pi 27y dy\\\\Volume = 27\pi \int _{0}^{1} \ ydy\\\\Volume = 27 \pi [\dfrac{y^2}{2}] _{0}^{1}$

$\rm Volume = 13.5 \times \pi \times [y^2] _{0}^{1}\\\\Volume = 13.5 \times \pi \times (1^2 - 0^2)\\\\Volume = 42.411 \ cubic \ units$

More about the integration link is given below.

brainly.com/question/18651211

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