Find a function that represents the amount of air required to inflate the spherical balloon from a radius of $r$ inches to a radius of $r + 1$ inches.

f (r) = \frac{3}{2} π (r^{2} - 3 r + 1)

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f (r) = \frac{3}{2} π (2 r^{2} + 3 r + 1)

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f (r) = \frac{4}{3} π (3 r^{2} + 3 r + 1)

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f (r) = \frac{4}{3} π (3 r^{2} + 2 r + 1)

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Solution

The correct option is C $f (r) = \frac{4}{3} π (3 r^{2} + 3 r + 1)$
The amount or volume of air required to inflate the spherical balloon from a radius of $r$ inches to a radius of $r + 1$ inches.
$V = \frac{4}{3} π [(r + 1)^{3} - r^{3}]$

$= \frac{4}{3} π [r^{3} + 3 r^{2} + 3 r + 1 - r^{3}]$

$= \frac{4}{3} π [3 r^{2} + 3 r + 1]$

So, Function $= f (r) = \frac{4}{3} π [3 r^{2} + 3 r + 1]$

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Find a function that represents the amount of air required to inflate the spherical balloon from a radius of r inches to a radius of r+1 inches.

The correct option is C f(r)=43π(3r2+3r+1)The amount or volume of air required to inflate the spherical balloon from a radius of r inches to a radius of r+1 inches.V=43π[(r+1)3−r3] =43π[r3+3r2+3r+1−r3] =43π[3r2+3r+1] So, Function =f(r)=43π[3r2+3r+1]

Find a function that represents the amount of air required to inflate the spherical balloon from a radius of $r$ inches to a radius of $r + 1$ inches.