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Chapter 9: Q 1. (page 757)

The cardioid defined by r = 1 + cos 胃 and its interior is

translated one unit perpendicular to the xy-plane to define a

鈥渃测濒颈苍诲别谤.鈥�

Find the volume of the cylinder.

Short Answer

Expert verified

Volume is 5 square units.

Step by step solution

01

Step 1. Given information

Cardioid isr=1+cos胃

02

Step 2. Explanation

Consider the equation of cardioid as r=1+cos胃

Volume of a cylinder =蟺r2hwhere r,hdenote radius, height respectively.

Interior of the cardioid is translated one unit perpendicular to the xy-plane to define a cylinder.

Volume width="116">=鈭�1+cos胃d胃

=5cubic units

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Most popular questions from this chapter

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.

胃=蟺4

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(卤伪,0), major axis4伪

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(0,卤伪), minor axis2伪

In Exercises 32鈥�47 convert the equations given in polar coordinates to rectangular coordinates.
胃=-蟺6

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

0,0
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