Question

this is a pretty complicated question if someone could explain it i would appreciate it

Answer 1

Does this have a figure?

Answer 2

its a cone and a sphere

Answer 3

im getting 4pisqrt(2)
but thats wrong

Answer 4

fx is (x)*sqrt(x^2+y^2)
and fy is (x)*sqrt(x^2+y^2)

Answer 5

yes that is what I got, for the outer surface of the sphere. Do they want to include the surface area of the inside of the sphere?

Answer 6

but the answer is wrong the correct answer is4π(2−2sqrt(2))

Answer 7

just to make sure I am interpreting the problem correctly, do they have a figure?

Answer 8

no they don't =(

Answer 9

the equation of a sphere is z^2+x^2+y^2=4 does this have anything to do with this prob??

Answer 10

I would use polar coordinates...

but I'll puzzle on this, and post something later.

Answer 11

alright thanks=)

Answer 12

First, you say
the correct answer is4π(2−2sqrt(2))

that gives a negative number

But if you use the idea that the surface of the sphere is the area of a set of "rings" with circumference r and surface area ds

Answer 13

it is

Answer 14

if we integrate from 0 to pi we get the surface area of a sphere, 4 pi r^2

Here we integrate from 0 to pi/4 where the sphere meets the cone
we get
\[ 2 \pi r^2 (1 - \frac{\sqrt{2}}{2}) \]
with r= 2 this is
\[ 8 \pi (1 - \sqrt{2}/2) \]
or
\[ 4 \pi (2 - \sqrt{2}) \]