Mathematics College

9. The radius of sphere is increasing at a rate of 3cm/minute. Find the rate of change of volume
when r=2cm *

V = 12
48л
16л
64 л
32T

9. The Radius Of Sphere Is Increasing At A Rate Of 3cm/minute. Find The Rate Of Change Of Volumewhen

Answers

Answer 1

Answer:

48π

Step-by-step explanation:

Given that,

The radius of the sphere is increasing at a rate of 3cm/minute, [tex]\dfrac{dr}{dt}=3\ cm/minute[/tex]

The volume of a sphere is given by :

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

Differentiating both sides wrt t.

[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r^2\times \dfrac{dr}{dt}\\\\=4\pi r^2\times \dfrac{dr}{dt}[/tex]

Put r = 2 cm and dr/dt = 3 cm/minute

So,

[tex]\dfrac{dV}{dt}=4\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt}=4\pi \times 2^2\times 3\\\\\dfrac{dV}{dt}=48\pi[/tex]

Hence, the correct option is (a) "48π".

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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