Answer:
A) 8π ft²/ft
B) 24π ft²/ft
C) 48π ft²/ft
Explanation:
Surface area of the spherical balloon is not clear here but it is supposed to be;
S = 4πr²
where:
r is the radius of the spherical balloon
So thus, the rate of change of the surface area of the spherical balloon by its radius will be:
dS/dr = 8πr
A) at r = 1ft;
dS/dr = 8 × π × 1
dS/dr = 8π ft²/ft
B) at r = 3 ft;
dS/dr = 8 × π × 3
dS/dr = 24π ft²/ft
C) at r = 6ft;
dS/dr = 8 × π × 6
dS/dr = 48π ft²/ft
