Question

The surface area S(r) (in square meters) of a spherical balloon with radius r meters is given by S(r) = 4ar". The radius Pt) in meters) after t seconds is given by Pt Write a formula for the surface area N (t) (in square meters) of the balloon after t seconds. It is not necessary to simplify. N(t) = 0 x s ?

Answer 1

I think there's a misunderstanding in the question. There seems to be a missing formula for the radius after t seconds symbolized by "Pt". In order to provide a formula for the surface area N(t), we need that information first.

However, assuming we have the formula for the radius after t seconds as Pt, here's how we can proceed:

1. We are given the surface area S(r) of a spherical balloon, which is represented by the formula S(r) = 4 * pi * r^2. This formula calculates the surface area of a sphere using the radius r.

2. Next, we're asked to find the formula for the surface area N(t) of the balloon, but using the time t instead of the radius r. To do so, we'll have to substitute the radius r in the surface area formula with Pt, which represents the radius of the balloon after time t.

So, by replacing r in the original formula with Pt, we get:

N(t) = 4 * pi * (Pt)^2

Without the specific formula for Pt, we can't simplify it further than this. However, this formula allows you to calculate the surface area of the balloon after t seconds, once you know how the radius changes with time.