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

$\boxed{\boxed{\text {Volume =} \dfrac{4}{3} \pi r^3}}$

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

$972\pi = \dfrac{4}{3} \pi r^3$

$r^3 = 972\pi \div \dfrac{4}{3} \pi$

$r^3 = 729$

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

$r = 9 \text{ mm}$

Find Circumference:

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

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

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

Answer 2

Answer:

18

Step-by-step explanation: