Help plz A sphere is rolled between two sharp, parallel blades that are 77 centimeters apart. Both blades cut off a piece of the sphere cleanly, leaving two parallel circular faces with radii of 39 and 60 cm. What is the radius of the sphere?

The radius of the sphere is approximately 62.71 cm

Step-by-step explanation:

The question relates to the definition of a sphere

The given parameters are;

The distance between the sharp parallel blades through which the sphere is rolled = 77 centimeters

The radii of the circular faces left by cutting the sphere with the blade = 39 cm  and 60 cm

From the triangles formed by the cross-section of the sphere, we have;

AB ║ DE Given

∠A ≅ ∠E, ∠D ≅ ∠B Alternate angles

∠C ≅ ∠C by reflective  property

∴ ΔABC ~ ΔDCE by Angle-Angle similarity theorem

CF/CG = AB/DE = 78/120 = 13/20

CF = CG × 13/20

CF + CG = 77

∴ CG × 13/20 + CG = 77

33·CG/20 = 77

∴ CG = 140/3

CF = 13/20 × CG = 13/20 × 140/3 = 91/3

CF = 91/3

The diameter of the sphere AE = AC + EC

By Pythagoras's theorem

AC = √(FA² + CF²) = √(39² + (91/3)²) = 13·√(130)/3

EC = √(CG² + GD²) = √((140/3)² + 60²) = 20·√(130)/3

∴ AE = AC + EC = 13·√(130)/3 + 20·√(130)/3 = 11·√(130)

The diameter, 'D', of the sphere, AE = 11·√(130)

The radius of the sphere = D/2 = 11·√(130)/2 ≈ 62.71 cm

the answer is 5636.7

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