Respuesta :

The surface area of the sphere in terms of t is N(t) = 64πt²/9 square meters.

What is a sphere?

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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