The cone equation gives

which means that the intersection of the cone and sphere occurs at

i.e. along the vertical cylinder of radius

when

.
We can parameterize the spherical cap in spherical coordinates by

where

and

, which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is

. So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

Now the surface area of the cap is given by the surface integral,




Answer:
4
Step-by-step explanation:
B = (6,5) C = (6,9)
√(x2 - x1)² + (y2 - y1)²
√(6 - 6)² + (9 - 5)²
√(0)² + (4)²
√16
= 4
Step-by-step explanation:
all work is pictured/shown
Answer is -pi
Let x be this unknown number. Adding on x to pi gets us the expression x+pi
If we set x+pi equal to zero (which is a rational number) and solve for x, we get
x+pi = 0
x+pi - pi = 0 - pi
x = -pi
so adding pi to -pi will lead to 0 since
x+pi = -pi+pi = 0