The 9 stands for hundredths
First, you have to find the equation of the perpendicular bisector of this given line.
to do that, you need the slope of the perpendicular line and one point.
Step 1: find the slope of the given line segment. We have the two end points (10, 15) and (-20, 5), so the slope is m=(15-5)/(10-(-20))=1/3
the slope of the perpendicular line is the negative reciprocal of the slope of the given line, m=-3/1=-3
step 2: find the middle point: x=(-20+10)/2=-5, y=(15+5)/2=10 (-5, 10)
so the equation of the perpendicular line in point-slope form is (y-10)=-3(x+5)
now plug in all the given coordinates to the equation to see which pair fits:
(-8, 19): 19-10=9, -3(-8+5)=9, so yes, (-8, 19) is on the perpendicular line.
try the other pairs, you will find that (1,-8) and (-5, 10) fit the equation too. (-5,10) happens to be the midpoint.
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,




5.7y-5.2=y/2.5
Add 5.2 to both sides:
5.7y = y/2.5 + 5.2
y/2.5 = 0.4y
5.7y = 0.4y + 5.2
Subtract 0.4y from both sides:
5.3y = 5.2
Divide both sides by 5.3:
y = 5.2/5.3
y = 0.98113