Answered: 2. Refer to the figure and find the…

2. Refer to the figure and find the volume obtained by rotating the given region about the specified line. R2 about BC а. R3 about OC C(0, 1) R2 B(1, 1) b. y = Vr R3 A(1, 0)

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.3: Cylinders And Cones

Problem 25E

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Question

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Please explain step by step in detail

2. Refer to the figure and find the volume obtained by rotating the given region about the
specified line.
R2 about BC
а.
yA
В(1, 1)
R3 about OC
C(0, 1)
R2
b.
y = %
R3
A(1, 0)

Expert Solution

Step 1

Given that, the radius $r = 1 - \sqrt[4]{x}$ and the region is lies between a=0 and b=1.

Obtain the area of the region $R_{2}$ .

$\begin{array}{rcl} A (x) & = & π {(1 - \sqrt[4]{x})}^{2} \\ = & π (1 + \sqrt{x} + 2 \sqrt[4]{x}) \\ = & π (1 + {(x)}^{\frac{1}{2}} + 2 {(x)}^{\frac{1}{4}}) \end{array}$

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