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.”

Surface area: Find the surface area of the cylinder.

Remember to include the top and bottom of the solid

in your calculations.

Short answer

Answer is 9 square units.

Step-by-step solution

Step 1. Given information

The cardioid defined by r = 1 + cos θ and its interior is translated one unit perpendicular to the xy-plane to define a “cylinder.”

Step 2. Explanation

The cardioid defined by r = 1 + cos θ and its interior is translated one unit perpendicular to the xy-plane to define a “cylinder.”

Surface area of a cylinder $=2\mathrm{\pi r}\left(\mathrm{r}+\mathrm{h}\right)$where $r,h$denote radius, height of a cylinder respectively.

So,

Surface area of a cylinder width="93">=∫1+cosθ

$=9$square units