Given: OK = 3.8, SK = 8.9 Find: V of the sphere

Question

Given: OK = 3.8, SK = 8.9

Find: V of the sphere

link to picture https://homework.russianschool.com/resource?key=00suo

Answer 1

Call the point where the sphere touches the cone T, and the center C.

Triangle STC is similar to triangle SOK

Therefore, SK/OK = SC/TC

TC is the radius of the sphere, so

SK/OK = SC/r

8.9/3.8 = 2.3421 = SC/r

SC + OC = SO

From the pythagorean theorem, you get that SO is 8.04798. Also OC is the radius of the sphere, so

SC + r = 8.04798

So you now have two equations with two unknowns:

2.3421 = SC/r

SC + r = 8.04798

Do you think you can solve the rest

OC is also the radius