Find the area outside the circle and inside the cardioid .
A) 7
E) 18.84

Question

Find the area outside the circle  and inside the cardioid  .
A) 7 
E) 18.84

Quizplus · Accepted Answer

Since the circle has radius 3 and the cardioid has a cusp at the origin, we can split the region into two parts: the region inside the circle but outside the cardioid, and the region inside the cardioid but outside the circle.

To find the area outside the circle but inside the cardioid, we can use the formula for the area of a cardioid:

A = (3/2)R^2

where R is the radius of the circle. Plugging in R = 3, we get:

A = (3/2)(3^2) = 13.5

To find the area inside the cardioid but outside the circle, we can use the formula for the area of a cardioid with a circular hole:

A = (3/2)R^2 - R^2/4

Plugging in R = 3, we get:

A = (3/2)(3^2) - (3^2/4) = 13.5 - 2.25 = 11.25

Therefore, the total area we want to find is:

A = 13.5 + 11.25 = 24.75

which is closest to choice B) 24.76.

Find the Area Outside the Circle and Inside the Cardioid