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.

Question

Mathematics

Dayton Sanford

19 October, 05:53

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.

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Answers (1)

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Gavyn Ellison · Answer 1

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)