Respuesta :

amyjess512

Answer:

512pi cubic inches a minute

Step-by-step explanation:

Hello, we would need the volume formula which would be:

V=4/3pi(r)^3

Here we are given the radius is 8 inches and the rate is 2 inches per minute, so we would just plug it in.

[tex]\frac{dV}{dt} = 4\pi(8)^{3} (2)\\= 8\pi * (8)^{3} \\8^3 =64\\\\8\pi * 64\\\\\frac{dV}{dt} = 512\pi[/tex]

512pi cubic inches a minute would be the answer

oscar236

Answer:

512π cubic inches/minute

Step-by-step explanation:

Volume V = 4/3 π r^3

dV / dr =   4 π r^2

dr/dt = 2

Rate of change of the Volume:

dV/dt = dV / dr  * dr/dt

= 4 π r^2 * 2

=   8 π r^2

When r = 8:

dV/dt = 8π(8)^2

= 512π cubic inches/minute

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