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Find the volume of the solid generated when the region bounded by y = 9x and y = 36/x is revolved about the x-axis.

Find the volume of the solid generated when the region bounded by y = 9x and y = 36/x is revolved about the x-axis.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question

6.3.23

--- **Use the general slicing method to find the volume of the following solid.** The solid with a semicircular base of radius 18 whose cross sections perpendicular to the base and parallel to the diameter are squares. --- ### 6.3.23 – Setup & Solve Find the volume of the solid generated when the region bounded by \( y = 9x \) and \( y = 36\sqrt{x} \) is revolved about the x-axis. **Graph/Diagram Explanation:** The graph illustrates the region \( R \) bounded by the two curves \( y = 9x \) and \( y = 36\sqrt{x} \). This area is shaded in the diagram. The x-axis is the line about which the region is revolved to form a solid. --- ### 6.3.47 For the region bounded by \( y = 8 - x^3 \), the x-axis, and y-axis, determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. ---
Transcribed Image Text:--- **Use the general slicing method to find the volume of the following solid.** The solid with a semicircular base of radius 18 whose cross sections perpendicular to the base and parallel to the diameter are squares. --- ### 6.3.23 – Setup & Solve Find the volume of the solid generated when the region bounded by \( y = 9x \) and \( y = 36\sqrt{x} \) is revolved about the x-axis. **Graph/Diagram Explanation:** The graph illustrates the region \( R \) bounded by the two curves \( y = 9x \) and \( y = 36\sqrt{x} \). This area is shaded in the diagram. The x-axis is the line about which the region is revolved to form a solid. --- ### 6.3.47 For the region bounded by \( y = 8 - x^3 \), the x-axis, and y-axis, determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. ---
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