Answer:
The volume of the sphere = 169.78 unit³
Step-by-step explanation:
The rest of the question is the attached figure.
As shown at the attached figure.
ΔKOS is a right triangle at O
KS is the hypotenuse
So, OS = √(KS² - OK²) = √(8.9² - 3.8²) = √64.77
let KS contact the sphere at P, and the center of the sphere is Q
So, both of KP and KO are a tanget to the sphere
∴ KP = OK = 3.8
As shown:
PQ // OK
So, [tex]\frac{KP}{KS} =\frac{OQ}{OS}[/tex]
∴ OQ = OS * KP/KS = √64.77 * 3.8/8.9 = 3.436
OQ is radius of the sphere
The volume of the sphere = V = (4/3) π r³ , π = 3.14
∴ V = (4/3) * 3.14 * (3.436)³ = 169.78 unit³
So, the volume of the sphere = 169.78 unit³
