Question

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?

Answer 1

R(t) = 6t 

putting into the formula 

V = (4/3) pi * r^3 

V(t) = (4/3) pi * (6t)^3 
 
V(t) = (4/3) pi * 216 t^3

Multiply the 4/3 by the 216 and 

V(t) = 288 * pi * t^3

Answer 2

Answer:

$S(t)=196\pi t^2$

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)=$4\pi R^2$

Substitute the value

$S(R(t))=S(t)=4\pi (7t)^2=196\pi t^2$

Hence, $S(t)=196\pi t^2$