Question

Hello, I need some helo with stereometry.

A sphere, which has a radius of 26, is being interesected by a plane, which is away of 10cm from the centre of the sphere. Find the cross sectional area. (I will add a picuture)

Answer 1

@stamp

Answer 2

do you have any ideas, @Meepi

Answer 3

Yeah, I'm just very bad at the drawing tool tho so it might look really ugly :p

Answer 4

haha dont worry, I am poor at drawing too!

Answer 5

You need to find the radius of the cross-sectional circle, so start by considering a cross-section of the sphere


We know the equation of the circle \(x^2 + y^2 = r^2\), so in this case it would be \(x^2 + y^2 = 26^2\)
We know that \(y = 10\), so we can solve for x and get the radius of the cross section and then calculate the area using \(\pi r^2\)

Answer 6

x stands for radius of a crossed sectional area?THANKS!

Answer 7

centimeters in this case

Answer 8

12th (the last one in high school)

Answer 9

It doesn't look like calculus to me

Answer 10

well, I am not from USA, so we don't have lessons like only calculus or algebra, geometry. It is just a topic of our math book: )

Answer 11

Find x

Answer 12

use x to obtain pi r ^ 2

Answer 13

well, thank you guys for your help a lot!

Answer 14

\[x=\sqrt{26^2-10
^2}\]\[x=24\]\[area=\pi x^2\]\[area=\pi
(24)^2\]

Answer 15

Notice that you dont even need pythagoream theorem because this is a 5:12:13 triangle

Answer 16

5:12:13 triangle

compare to

10:x:26 triangle

well x = 2(12) = 24

Answer 17

and then yeah area is just based off that radius of 24

Answer 18

well, it is much easier for me to use phytagoream theoremus. what is about that 5:12:13 triangle?

Answer 19

3:4:5 triangles, 5:12:13 triangles

it is something u are supposed to know

Answer 20

well, I don't. or maybe we call it in another way

Answer 21

What is h?



h = 5

Answer 22

What is x?



x = 4

Answer 23

What is x?



x = 3