Mathematics: Suppose the radius of the sphere is increasing at a constant rate of 0.3 centimeters per second. at the moment when the radius is 24 centimeters, the volume is increasing at a rate of?

8.8 x 10^3 / 2.9 x 10^3 = 3.03...

Suppose the radius of the sphere is increasing

Ответ:

meme2186

16.01.2022

Mathematics

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

Step-by-step explanation:

We have equation for volume of a sphere

$V=\frac{4}{3}\pi r^3$

where r is the radius

Differentiating with respect to time,

$\frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}$

Given that

Radius, r = 24 cm

$\frac{dr}{dt}=0.3cm/s$

Substituting

$\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min$

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

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Suppose the radius of the sphere is increasing at a constant rate of 0.3 centimeters per second. at the moment when the radius is 24 centimeters, the volume is increasing at a rate of?

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