Let f(x) = √√9x-x² and let R be the region bounded by the graph of f and the x-axis on the interval [0,5]. a. Find the area of the surface generated when the graph of f on [0,5] is revolved about the x-axis. b. Find the volume of the solid generated when R is revolved about the x-axis. a. Find the area of the surface. square units. (Type an exact answer, using as needed.) b. Find the volume of the solid. cubic units.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Let
f(x)=√√9x-x²
and let R be the region bounded by the graph off and the x-axis on the interval [0,5].
a. Find the area of the surface generated when the graph of f on [0,5] is revolved about the x-axis.
b. Find the volume of the solid generated when R is revolved about the x-axis.
a. Find the area of the surface.
square units.
(Type an exact answer, using as needed.)
b. Find the volume of the solid.
cubic units.
(Type an exact answer, using as needed.)
Transcribed Image Text:Let f(x)=√√9x-x² and let R be the region bounded by the graph off and the x-axis on the interval [0,5]. a. Find the area of the surface generated when the graph of f on [0,5] is revolved about the x-axis. b. Find the volume of the solid generated when R is revolved about the x-axis. a. Find the area of the surface. square units. (Type an exact answer, using as needed.) b. Find the volume of the solid. cubic units. (Type an exact answer, using as needed.)
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