Question

The functions r = f(t) and V = g(r) give the radius and the volume of a commercial hot air balloon being inflated for testing. The variable t is in minutes, r is in feet, and V is in cubic feet. The inflation begins at t = 0. Give a mathematical expression that represents the given statement. The volume of the balloon if its radius were twice as big.

Answer 1

Answer:

V=g(2r)

Step-by-step explanation:

Since volume is a function of radius, we input 2r in the given function V=g(r).

As given in the question "The volume of the balloon if its radius were twice as big?".

• Assuming the commercial balloon is spherical in shape when inflated.
• Volume of sphere, V=4/3 πr³
• Put r= 2r in the above equation, we get:

V= 32/3 πr³ ≡ g(2r)