Question

Could someone help plz

Answer 1

Answer:

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