Final answer:
The radius of the sphere is 9 cm. The circumference is 18(π) cm, and the volume of the sphere is 972(π) cm³.
Step-by-step explanation:
The given ratio of surface area to volume for a sphere is 1:3 cm.
Using the formulae for a sphere:
volume = 4/3 (π) (r)³ and surface area = 4 (π) (r)², we can set up an equation to find the radius of the sphere.
Firstly, we know that the surface area to volume ratio for a sphere is surface area/volume, which is (4 (π) (r)²)/(4/3 (π) (r)³) = 3/r.
Given the ratio is 1:3 cm, we have 1:3 cm = 3:(r) cm, implying r = 9 cm.
Once we have the radius, we can find the circumference of the sphere using the formula
Circumference = 2(π)r, which is 2(π)(9 cm) = 18(π) cm.
Next, for the volume, we substitute r into the volume formula to get
Volume = 4/3 (π) (9 cm)³
= 4/3 (π)(729 cm³)
= 972(π) cm³.