Calculus problem...please help?

Question

A balloon with a radius of r inches has a volume V(r )= 4/3πr^3. Find a function that represents the amount of air required to inflate the balloon from a radius of r to a radius of r+1 inches.

Answer 1

That would simply be [V(r + 1) - V(r)].

V(r + 1) = (4/3)π(r + 1)^3

V(r + 1) - V(r)
= (4/3)π(r + 1)^3 - 4/3πr^3
= (4/3)π [(r + 1)^3 - r^3]
= (4/3)π [(r^3 + 3r + 3r^2 + 1) - r^3]
= (4/3)π [(3r + 3r^2 + 1)]

Answer 2

Voriginal = (4/3)pi r^3
Vnew = (4/3)pi (r+1)^3
Amount of air, ignoring the compression of the air by the ballon material as it increases, is the difference:
Vnew - Voriginal = (4/3)pi[(r+1)^3 - r^3]
(r+1)^3 = (r^2+2r+1)(r+1) = r^3+r^2+2r^2+2r+r+1 = r^3+3r^2+3r+1
Vnew - Vorig = (4/3)pi[3r^2+3r+1]
Call the function V(r) = (4/3)pi[3r^2+3r+1]

Answer 3

V(r) = 4/3 πr^3
V(r+1) = 4/3 π(r+1)^3

Volume of air required (Va) = V(r+1) - V(r)
Va = 4/3 π(r+1)^3 - 4/3 πr^3
Va = 4/3π((r+1)^3 - r^3)
Va = 4/3π(r^3 + 3r^2 + 3r +1 - r^3)
Va = 4/3π(3r^2+3r+1)

Answer 4

f(r) = V(r+1) - V(r)
f(r) = 4π(r+1)³/3 - 4πr³/3
f(r) = (4π/3)[ r³ + 3r² + 3r + 1 - r³]
f(r) = (4π/3)[3r² + 3r + 1]
f(r) = 4πr² + 4πr + 4π/3

Answer 5

what ^ they said. lol.
....idk im not in calc. im stupid :/