Air Intake Manifold Lab
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Lesson Summary:
In this lesson, Professor Perez teaches how to find the volume and surface area of a region bounded by curves using the example of an air intake manifold. Through circular cross-sections and integration techniques, he breaks down the math into manageable steps, showing how to find the area of inlets and outlets, and ultimately the volume and surface area of the manifold. With clear explanations and helpful tips, this lesson is a great resource for anyone looking to improve their calculus skills.
Lesson Description:
Finding the volume and surface area of a region bounded by curves.
Created by and copyright of Larry Perez. Funded by the state of California through Saddleback College. More information on videos, resources, and lessons at Algebra2Go.
Questions answered by this video:
- How can you calculate the volume and surface area of an air intake manifold?
- How can you find the area of the region bounded by the x-axis, lines x = ln (1/2), x = ln 2, and the curve f(x) = e^x?
- How do you find the volume of the manifold generated by semicircular cross-sections whose radii is equal to the length of the partitions that are perpendicular to the x-axis and bounded between the x-axis and the function f(x) = e^x?
- How do you find the intersection between the line x = ln2 and the curve f(x) = e^x?
- How do you find the intersection between the line x = ln (1/2) and the curve f(x) = e^x?
- What is the formula for the surface area of revolution?
- How do you find the surface area of a curve rotated around the x-axis?
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Staff Review
This lesson solves a rather complicated problem of finding the volume and surface area of a region bounded by several lines and curves that is rotated around the x-axis to form an air intake manifold. This is a very applied problem with some very involved formulas and calculations in it.
