2 years ago

HALP PLLLLLLZZZZZZZ ILL GIVE U BRAINLIEST!!

Mathematics

1 answer:

insens350 [35]2 years ago

8 0

The answer to your question is A

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The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing (in mm3/s) when the diameter is 40 m

daser333 [38]

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$\dfrac{dV}{dt}=502.65\ mm^3/s$

Step-by-step explanation:

The volume of a sphere is given by :

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$\dfrac{dV}{dt}=\dfrac{d}{dt}(\dfrac{4}{3}\pi r^3)\\\\\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r\times \dfrac{dr}{dt}$

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$\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3\times 20\times 2\\\\=502.65\ mm^3/s$

So, the volume is increasing at the rate of $502.65\ mm^3/s$ .

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