Question

Write down the name of the curves and shade the region that is inside of r= 8 and to the left of r= - 4 sec 0. Hence, find the area of the shaded region.

Answer 1

The shaded region is the area of a circle with radius 4.

Step-by-step explanation:

To find the area of the shaded region, we first need to identify the curves described by the equations given. The equation r = 8 represents a circle with radius 8, centered at the origin, while the equation r = -4sec(0) represents a curve that is symmetric to the y-axis. This curve is a circle with center at (-2,0) and radius 4. To shade the region that is inside of r = 8 and to the left of r = -4sec(0), we need to find the region where these curves overlap. Since the circle with radius 4 is entirely inside the circle with radius 8, the shaded region is the area of the circle with radius 4.

To find the area, we use the formula for the area of a circle: A = πr^2. Substituting the radius 4 into the formula, we get A = π(4)^2 = 16π square units.