Respuesta :
Given, the surface area of a sphere is = [tex] 324\pi cm^2 [/tex]
The formula to find the surface area of a sphere = [tex] 4\pi r^2 [/tex]
Where, r is the radius of the sphere.
As the surface area of the sphere given, we can equate it with the formula.
So we can write the equation as,
[tex] 4\pi r^2=324\pi [/tex]
To find r, first we have to move 4 to the right side by dividing it to both sides. We will get,
[tex] (4\pi r^2)/4 = (324\pi )/4 [/tex]
[tex] \pi r^2 = (324\pi )/4 [/tex]
[tex] \pi r^2 = 81\pi [/tex]
Now to find r, we have to move [tex] \pi [/tex] to the right side, by dividing it to both sides. We will get,
[tex] (\pi r^2)/\pi =(81\pi )/\pi [/tex]
[tex] r^2 = 81 [/tex]
Now to find r, we will take square root to both sides.
[tex] \sqrt{r^2} = \sqrt{81} [/tex]
[tex] r = 9 [/tex]
So we have got the radius of the sphere = 9cm.
Now the formula to find the volume of the sphere = [tex] (\frac{4}{3})\pi r^3 [/tex]
Now plugging in the value of r we will get,
Volume = [tex] \frac{4}{3} \pi r^3 [/tex]
= [tex] \frac{4}{3}\pi (9)^3 [/tex]
=[tex] \frac{4}{3}\pi (729) [/tex]
=[tex] \frac{(4)(729\pi)}{3} [/tex]
=[tex] \frac{(2916\pi)}{3} [/tex]
= [tex] (972\pi ) [/tex]
So the required volume of the sphere = [tex] 972\pi cm^3 [/tex]
