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How fast is the radius changing when diameter of the snowball is 10 cm given a spherical snowball with an outer layer of ice melts so that the volume of the snowball decreases at a rate of 2cm per 3min?

Answer 1

Elijah Abram

You can try this:

(check my maths anyway!!! Hope it helps)

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Answer 2

Paisley Johnson

The radius is decreasing at a rate of #0.0021"cm/min"#

We need to find #(dr)/(dt)#

We know #(dV)/(dt)=-2/3=-0.66cm^(3)permin#

So lets set up:

#(dr)/(dt).(dV)/(dr)=(dV)/(dt)#

#V=4/3pir^3#

So #(dV)/(dr)=4pir^2#

So:

# (dr)/(dt).4pir^2=-0.66#

#(dr)/(dt)=-(0.66)/(4xx3.142xx5^2)#

#(dr)/(dt)=-0.0021"cm/min"#

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Answer 3

Isaiah Allen

The radius of the snowball is changing at a rate of ( \frac{-1}{3\pi} ) cm/min when the diameter is 10 cm.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.