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A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 7 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S(0) = 0.) . S(t) = cm^2?

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Answer:

[tex]S(t)=196\pi t^2[/tex]

Step-by-step explanation:

We are given that

Radius of balloon increasing at the rate= 7 cm/s

Let time= t seconds

In 1 second radius  =7 cm

In t second radius =R(t) = 7 t

We have to find the surface area of  balloon as  function of time t

We know that area of sphere=S(R)=[tex]4\pi R^2[/tex]

Substitute the value

[tex]S(R(t))=S(t)=4\pi (7t)^2=196\pi t^2[/tex]

Hence, [tex]S(t)=196\pi t^2[/tex]

The surface area of the spherical ballon, in centimeters squared, is given by:

[tex]S = 196\pi t^2[/tex]

What is the surface area of a sphere?

The surface area of a sphere of radius r is given by:

[tex]S = 4\pi r^2[/tex]

In this problem, the radius of the balloon is increasing at the rate of 7 cm/s and the initial surface area is of 0, hence:

[tex]r = 7t[/tex]

Thus, the surface area is given by:

[tex]S = 4\pi r^2[/tex]

[tex]S = 4\pi (7t)^2[/tex]

[tex]S = 196\pi t^2[/tex]

More can be learned about the surface area of a sphere at https://brainly.com/question/1658430

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