Question

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

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

“cylinder.”

Find the volume of the cylinder.

Short answer

Volume is 5 square units.

Step-by-step solution

Step 1. Given information

Cardioid is$r=1+\cos \theta$

Step 2. Explanation

Consider the equation of cardioid as $r=1+\cos \theta$

Volume of a cylinder $=\pi r^{2}h$where $r,h$denote radius, height respectively.

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

Volume width="116">=∫1+cosθdθ

$=5$cubic units