Answer:
Find the perimeter
2 answers:
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Answer:
33.85 units^2
Step-by-step explanation:
you must first draw the triangle on the plane using the equations (see
attached file), you will have a right angle triangle with a height of 192 and a base of 6.
then you calculate the angle with the tangent function = 88.21
Then you use the small triangle to find the value of a (see attached file).
Finally, you propose an equation for X to find one of the sides of the triangle, once you have x squared it, and you already have the area,
i attached procedure
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,
which means that the intersection of the cone and sphere occurs at
i.e. along the vertical cylinder of radius
We can parameterize the spherical cap in spherical coordinates by
where
Now the surface area of the cap is given by the surface integral,