3 years ago

I need helpppppppp!!!!

1 answer:

kati45 [8]3 years ago

8 0

What do you need help with?

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drek231 [11]

Answer:

The answer is $\frac{3}{10\pi } cm/min$

Step-by-step explanation:

Assuming the snowball is a perfect sphere, then if A denotes the surface area and D the diameter then:

$A=4\pi r^{2} = 4\pi (\frac{D}{2} )^{2} =\pi D^{2}$

Differentiating wrt r we have:

$\frac{dA}{dD} =2\pi D$

We are told that $\frac{dA}{dt}= -6$ and we want to find $\frac{dD}{dt}$

By the chain rule we have:

$\frac{dA}{dD}=\frac{dA}{dt}.\frac{dt}{dD}=\frac{\frac{dA}{dt} }{\frac{dD}{dt} }$

∴ $2\pi D=-\frac{6}{\frac{dD}{dt} }$

∴ $\frac{dD}{dt}=-\frac{6}{2\pi D}$

When D=10 then

$\frac{dD}{dt} =-\frac{6}{10*2\pi } =-\frac{3}{10\pi }$

The sign (-) shows that the D is decreasing.

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3 years ago