QUESTION - At a frozen yogurt store, customers are given the option of a juice-filled gelatin sphere as a yogurt topping. Each sphere contains 36π cubic millimeters of juice. Which statements are accurate?A) The radius of the sphere is 3 millimeters.B) The circumference of the sphere is 6π millimeters.C) The radius of the sphere is 9 millimeters.D) The circumference of the sphere is 18π millimeters.E) The radius of the sphere is 12 millimeters.F) The circumference of the sphere is 24π millimeters.
Accepted Solution
A:
Answer:A) The radius of the sphere is 3 millimeters.B) The circumference of the sphere is 6π millimeters.Step-by-step explanation:Based on the answer selections, it appears we need to find the radius and circumference of the sphere. We can start with the volume formula in terms of the radius: V = (4/3)πr³ 36π = (4/3)πr³ (36π)(3/(4π)) = r³ = 27 . . . . . . mm³ r = ∛27 = 3 . . . . mm³Then the circumference is ... C = 2πr = 2π(3 mm) = 6π mmThe radius is 3 mm; the circumference is 6π mm.