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:
11.5
Step-by-step explanation:
3 x 3 5/6
3 x 23/6
=69/6
=11.5
Answer:
(-11, 1)
Step-by-step explanation:
x-values are horizontal and y-values are vertical
so add -4 to -7 to get -11
add 0 to 1 to get 1
new point is at (-11,1)
42 ÷ 63
63 -> 420
63x6=378
420-378=42
63->420
So, how many times does 63 go into 42? Well, it doesn't. So put down a zero on your paper, and then a decimal. So if we add a zero onto 42, it becomes 420. Well, 420 is divisible by 63. In fact, 63 goes into 420 6 times, making a total of 378. 420-378 = 42. Then the process begins again. So you've got a 0.6, and that six just keeps on repeating. On paper, you're gonna wanna put a dash over the six to show that it's repeating.
Anyways, the answer is .66 repeating.