Word Problem involving composition of two functions! 15 pts for an answer

The surface area of the sphere in terms of t is N(t) = 64πt²/9 square meters.
It is defined as three-dimensional geometry when half-circle two-dimensional geometry revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
We have:
[tex]\rm S(r) = 4\pi r^2[/tex]
The radius:
[tex]\rm P(t) = \dfrac{4}{3}t[/tex]
Plug the value of radius in the surface area formula:
[tex]\rm N(t) = 4\pi (\dfrac{4}{3}t)^2[/tex]
[tex]\rm N(t) = 4\pi (\dfrac{16}{9}t^2)\\\\\rm N(t) = \dfrac{64}{9} \pi t^2[/tex]
Thus, the surface area of the sphere in terms of t is N(t) = 64πt²/9 square meters.
Learn more about the sphere here:
brainly.com/question/11374994
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