Question

The volume of a sphere is 972π cubic millimeters. What is the circumference of the great circle of the sphere? (Recall that the formula for the volume for a sphere is v=4/3π^3 and the formula for the circumference of the great circle is C=2πr.)

A. 9π mm
B. 18π mm
C. 36π mm
D. 162π mm

Answer 1

18

Explanation:

Answer 2

`\boxed{\boxed{\text {Volume =} (4)/(3) \pi r^3}}`

Given that the volume is 972π mm³, find radius:


`972\pi = (4)/(3) \pi r^3`


`r^3 = 972\pi / (4)/(3) \pi`


`r^3 = 729`


`r = \sqrt[3]{729}`


`r = 9 \text{ mm}`

Find Circumference:


`\boxed { \boxed {\text{Circumference = }2 \pi r}}`


`\text{Circumference = }2 \pi (9)`


`\text{Circumference = }18 \pi \text{ mm}`