At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Explore our Q&A platform to find reliable answers from a wide range of experts in different fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.
Sagot :
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.
[tex]\rm x = 3\sqrt{3y} \ or \ x^2 = 27y[/tex]
x = 0, and y = 1
Then the volume of the solid will be
[tex]\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}\\\\[/tex]
[tex]\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[/tex]
More about the integration link is given below.
https://brainly.com/question/18651211
#SPJ4
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.
