Question

The ratio of the radii of two spheres is 3:1. The volume of the larger sphere is 729 in3. What is the volume of the smaller sphere?
243 in3

81 in3

54 in3

27 in3

Answer 1

The volume of the sphere:
V = 4/3 · r³ π
The larger sphere:
729 = 4/3 · r³ · 3.14
r³ = ( 729 · 3 ) : ( 4 · 3.14 )
r³ = 174
r ( larger ) = ∛174 = 5.6 in
r ( smaller ) = 5.6 : 3 = 1.867 in
V ( smaller ) = 4/3 · 1.867³ · 3.14 = 27.246 ≈ 27 in³
Answer:
D ) 27 in³