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Likurg_2 [28]2 years ago

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The answer is A for this problem

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Answer:

The rate of decrease is: $43.2mm^3/min$

Step-by-step explanation:

Given

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Required

Rate of decrease when: $l = 18mm$

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Differentiate

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Make dV the subject

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Divide both sides by dt

$\frac{dV}{dt} = 3l^2 \cdot \frac{dl}{dt}$

Given that: $l = 18mm$ and $\frac{dl}{dt} = -0.8mm/min$

$\frac{dV}{dt} = 3 * (18mm)^2 * (-0.8mm/min)$

$\frac{dV}{dt} = 3 * 18 *-0.8mm^3/min$

$\frac{dV}{dt} = -43.2mm^3/min$

<em>Hence, the rate of decrease is: 43.2mm^3/min</em>

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