MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

[tex]\boxed{\boxed{\text {Volume =} \dfrac{4}{3} \pi r^3}}[/tex]

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

[tex]972\pi = \dfrac{4}{3} \pi r^3[/tex]

[tex]r^3 = 972\pi \div \dfrac{4}{3} \pi[/tex]

[tex]r^3 = 729[/tex]

[tex]r = \sqrt[3]{729} [/tex]

[tex]r = 9 \text{ mm}[/tex]

Find Circumference:

[tex]\boxed { \boxed {\text{Circumference = }2 \pi r}}[/tex]

[tex]\text{Circumference = }2 \pi (9)[/tex]

[tex]\text{Circumference = }18 \pi \text{ mm} [/tex]

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

[tex]972\pi = \dfrac{4}{3} \pi r^3[/tex]

[tex]r^3 = 972\pi \div \dfrac{4}{3} \pi[/tex]

[tex]r^3 = 729[/tex]

[tex]r = \sqrt[3]{729} [/tex]

[tex]r = 9 \text{ mm}[/tex]

Find Circumference:

[tex]\boxed { \boxed {\text{Circumference = }2 \pi r}}[/tex]

[tex]\text{Circumference = }2 \pi (9)[/tex]

[tex]\text{Circumference = }18 \pi \text{ mm} [/tex]