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- #1

#### karush

##### Well-known member

- Jan 31, 2012

- 3,241

I know this is a simple problem but new at it. answer not in book so hope correct.

- Thread starter karush
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- Thread starter
- #1

- Jan 31, 2012

- 3,241

I know this is a simple problem but new at it. answer not in book so hope correct.

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- #2

You have the formula for volume:

\(\displaystyle V=s^3\)

Differentiating with respect to time $t$, we find:

\(\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}\)

Now plug in the given data...and keep in mind your units...you should get \(\displaystyle \frac{\text{cm}^3}{\text{s}}\)

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- #3

- Jan 31, 2012

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$$3\cdot 2^2 \cdot 6 = 72 \text { cm}^3\text{/ sec}$$

and

$$3\cdot 10^2 \cdot 6 = 1800 \text { cm}^3\text{/ sec}$$

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- #4

Looks good. If you wish to be absolutely clear on an exam, I would write (in addition to showing your differentiation with respect to $t$ to obtain the formula):$$3\cdot 2^2 \cdot 6 = 72 \text { cm}^3\text{/ sec}$$

and

$$3\cdot 10^2 \cdot 6 = 1800 \text { cm}^3\text{/ sec}$$

a) \(\displaystyle \left. \frac{dV}{dt} \right|_{s=2\text{ cm}}=3\left(2\text{ cm} \right)^2\left(6\,\frac{\text{cm}}{\text{s}} \right)=72\,\frac{\text{cm}^3}{\text{s}}\)

b) \(\displaystyle \left. \frac{dV}{dt} \right|_{s=10\text{ cm}}=3\left(10\text{ cm} \right)^2\left(6\,\frac{\text{cm}}{\text{s}} \right)=1800\,\frac{\text{cm}^3}{\text{s}}\)

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- #5

- Jan 31, 2012

- 3,241

makes sense

I will post some more to see how close I am