Question

Sketch a graph of the polar equation and find the length and area of the curve in one loop.

Answer 1

Solution 

We will multiply A by two because the above calculation only half of area.\\

Therefore, A=4 \pi (unit area).

Therefore, the length of (b) is L=4 \pi unit length

Therefore, the area of (c) is A=\frac{3 \pi}{2} unit area

Therefore, the length of (c) is L=8 unit length

Therefore, the length of (d) is L \approx 12 \pi unit length