Question

Given: OK = 3.8, SK = 8.9

Find: V of the sphere

Answer 1

The volume of the sphere = 169.78 unit³

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,
`(KP)/(KS) =(OQ)/(OS)`

∴ 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