Question

Triangle ABC is a 45 degree-45 degree-90 degree in a sphere such that B is the center of the sphere and A and C are points on the sphere. Given the hypotenue of (trangle)ABC is 8√2 units, what is the surface area of the sphere?
A.) 320π square units
B.)85π square units
C.)256π square units
D.) 192π square units
The pic is there shown when you click on the question...Please help me

Answer 1

okay, that image was not that helpful. What are the special properties on a 45-45-90 triangle?

Answer 2

i dont get what you asking

Answer 3

What is special about having a triangle ABC that is a 45 degree-45 degree-90 degree?

Answer 4

It's a special triangle, correct?
http://www.regentsprep.org/Regents/math/algtrig/ATT2/Ltri45.htm

Answer 5

yess

Answer 6

thats right

Answer 7

so we know the hypotenuse. Therefore we can figure out the radius (as it's the legs of the triangle). Then from the radius we know the sphere's surface area equation. Get it?

Answer 8

okay so i got D is that correct?

Answer 9

erm... I got something else.

Answer 10

what did you get... I am confused lol

Answer 11

Okay. You have the hypotenuse is 8Sqrt[2]
so the leg is simply 8.
Then we use the equation for surface area of a sphere (or derivative of the volume equation)

Answer 12

then we get 256pi or C

Answer 13

can you explain that?

Answer 14

Okay

Answer 15

\[Surface Area= 4\pi r^2\]
So we plug in r=8; 4*8^2= 4*64=256
We ignored the pi initially since we realized that the pi was already built into the answers. Then we get 256pi or answer C

Answer 16

ohhh thanks so much :)