Question

The surface area Sr (in square meters) of a spherical balloon with radius r meters is given by =Sr4πr2. The radius Pt (in meters) after t seconds is given by =Pt73t. Write a formula for the surface area Nt (in square meters) of the balloon after t seconds. It is not necessary to simplify.

Answer 1

Explanation:

It is given that,

The surface area of a spherical balloon with radius r meters is given by :

$s(r)=4\pi r^2$

The radius P(t) (in meters) after t seconds is given by, P(t) = 73 t.

We need to write the surface area N(t) (in square meters) of the balloon after t seconds.

$s(r)=4\pi [P(t)]^2$

$s(r)=4\pi [73t]^2$

$s(r)=21316\pi t^2$

So, the surface area of the balloon is $21316\pi t^2$. Hence, this is the required solution.