Question

The figure shows a vertical cross section of a sphere inscribed in a right cone.
Find the volume of the sphere in terms of π.

Answer 1

@perl

Answer 2

@IrishBoy123 ?

Answer 3

@aaronq @hartnn

Answer 4

volume of a sphere = 4/3*pi*r^3

Answer 5

i dont know how to find the radius

Answer 6

tan angle = 12/5
angle at center = 2 * (tan^-1 (12/5)) = 135

Answer 7

so is the radius 135?

Answer 8

no I said angle

Answer 9

just realized this is a cone too

Answer 10

oh ok..

Answer 11

area of sector = pi * r * l
l = 13
135/360* pi *r^2

Answer 12

can someone explain to me how to find the radius?

Answer 13

we can note that:

triangles CKB and COD are similar each other, furthermore we can apply the theorem of Pitagora, so we get:
BC=sqrt(144+25)=13
Now we can write this proportion:
\[\begin{gathered}
OC:r = BC:HB \hfill \\
\left( {CK + r} \right):r = 13:5 \hfill \\
\end{gathered} \]
Now I apply the componendo property, so I get:
\[\begin{gathered}
CK:x = 8:5 \hfill \\
\left( {12 - 2r} \right):r = 8:5 \hfill \\
\end{gathered} \]

Answer 14

now, please apply the fundamental property of proportion, to get the value of r

Answer 15

@Michele_Laino CKB is not a triangle do you mean CHB?
can you please show how you got 8?

Answer 16

* why 13-5

Answer 17

oops.. I have made a typo, it is:
"triangles CHB and COD are similar each other..."

Answer 18

In general if I have this proportion:
A:B=C:D
then I can write:
(A-B):A=(C-D):C

Answer 19

I have used x in my computation by hand, you have to replace x with r

Answer 20

another result is:
(A-B):B=(C-D):D

Answer 21

@Michele_Laino thanks

Answer 22

thanks!