Answer:
True
Step-by-step explanation:
Given
Shape: Sphere
[tex]Volume = 972\ pi[/tex]
[tex]Area = 324\pi[/tex]
Required
True or False
The volume of a sphere is:
[tex]Volume = \frac{4}{3}\pi r^3[/tex]
Substitute [tex]972\pi[/tex] for volume
[tex]972\pi = \frac{4}{3}\pi r^3[/tex]
[tex]972 = \frac{4}{3}r^3[/tex]
Make r the subject
[tex]r^3 = \frac{3}{4} * 972[/tex]
[tex]r^3 = \frac{3 * 972}{4}[/tex]
[tex]r^3 = \frac{2916}{4}[/tex]
[tex]r^3 = 729[/tex]
[tex]r =9[/tex]
The surface area is calculated using:
[tex]Area =4\pi r^2[/tex]
[tex]Area =4\pi *9^2[/tex]
[tex]Area =4\pi *81[/tex]
[tex]Area =324\pi[/tex]
