Question

A sphere with radius 14 km is cut by a plane that is 6 km
above its center. Give an approximation of the area of the circle formed by
the intersection of the plane and the sphere.
http://i.imgur.com/kcXedHC.png


Which formula should be used to solve this? **Options in picture**
http://i.imgur.com/iW7uWCT.png ( i think its D is that correct)

What is the formula for the Surface Area of a Pyramid? (I think its C is that correct?)
http://i.imgur.com/4eGxKmt.png

Answer 1

for the first question, use the pythagorean theorem. for the second, I believe you are correct.

Answer 2

Could you show me how to use it?
Thats were I always fail, or the equation?

Answer 3

so you have a right triangle with side lengths r, x, and y.
do you know the length of r?
do you know the length of x?
do you know the length of y?

Answer 4

No i don't know any of the measurements

Answer 5

really? think again. what numbers are you given?

Answer 6

14 and 6

Answer 7

what is 14? does it happen to be r, x, or y? what is 6? does it happen to be r, x, or y?

Answer 8

Im not sure is 14 x?

Answer 9

is 6 y?

Answer 10

no... what is 14?

Answer 11

the radius of the sphere

Answer 12

ok. look on the picture. what letter represents the radius of the sphere?

Answer 13

Im not sure i thought the point for x did

Answer 14

it's r. look at the image lol, r goes from the center of the sphere to a point on the sphere, so it is the radius by definition

Answer 15

x isn't the point, x is a label for one of the line segments

Answer 16

oh my I told you Im horrible gahh

Answer 17

you're fine lol. but anyways, let's see if we can figure out what the number 6 means

Answer 18

So, 14 is r, is 6 y?

Answer 19

careful. 6 is the distance the plane is above the center of the sphere, correct?

Answer 20

oh yes

Answer 21

so would it be x.... Im guessing

Answer 22

yup. since x in this image is the distance from the center the plane is.

Answer 23

so with the pythagorean theorem, what can we deduce?

Answer 24

that a2+b2+c2, but i don't now how to put them into the equation

Answer 25

=c2 i meant

Answer 26

yeah. so just know that a and b are the legs , and c is the longest side or hypotenuse (which is opposite the 90 degree angle). so can you figure out how to put the numbers into the equation?

Answer 27

6^2+y^2=14^2?

Answer 28

yes.

Answer 29

so solve for y, and we have the radius of the circle

Answer 30

btw when I said your second formula was correct I acutally meant your third.

Answer 31

Oh okay i was like waaattt :)

Answer 32

Im don't know how to solve it to be honest with you... :(

Answer 33

I*

Answer 34

well, 6^2+y^2=14^2
now simplify as much as you can
36+y^2=196
isolate the variable
y^2=160
now find the square root
y=sqrt(160)
a negative square root makes no sense for length, so we take the positive.
simplify the radical
\(\Huge y=4\sqrt{10}\)

Answer 35

@inkyvoyd you are an angel

Answer 36

that is also why i can't see you im guessing, don't lie

Answer 37

thanks :)
anyways note that that's the radius, and you need the actual area of the circle

Answer 38

Oh lol, i always do that , always ugh.
So, now what?

Answer 39

take A=pi*r^2; you already found r=4sqrt(10). and for the second part, just put in the values for r and x and see which one works out to the answe ryou get for the area. I got B for the second

Answer 40

so the equation is A=3.14*4sqrt(10)^2?

Answer 41

yes but makes ure the 4sqrt(10) is in parenthesis cause it's the whole thing that's the radius

Answer 42

anyways, I think you should be able to get the rest... I must sleep. good luck!

Answer 43

Okay, thank you so much, have a nice night!!

Answer 44

you too :)