Find the area of inside and outside by sketching the graph of the equations using the graphing utility.

Question

Find the area of inside  and outside  by sketching the graph of the equations using the graphing utility. ​

Quizplus · Accepted Answer

Sketching the graph of the equations using a graphing utility, we can see that both equations represent circles. The first equation, 11eac44f_ebea_691b_bedf_df6bdbe36b0a_TB7497_11, has a radius of 6 and a center at (3,-2). The second equation, 11eac44f_ebea_902c_bedf_a58af6c005be_TB7497_11, has a radius of 3 and a center at (3,1). The area inside the first circle but outside the second is the area of the annulus formed by subtracting the smaller circle from the larger circle. 
Using the formula for the area of an annulus, A = π(R^2-r^2), where R is the radius of the larger circle and r is the radius of the smaller circle, we get:
A = π((6)^2-(3)^2)
A = π(36-9)
A = π(27)
A = 27π

Therefore, the best choice is C.

Find the Area of Inside and Outside by Sketching