Chapter 3: Q. 16 (page 299)

Suppose the radius r, height h, and volume V of a cylinder are functions of time t. How is $\frac{d V}{d t}$ related to $\frac{d h}{d t}$ if the radius of the cylinder is constant?

Short Answer

Expert verified

The derivatives $\frac{d V}{d t}$ and $\frac{d h}{d t}$ are related by $\frac{d V}{d t} = {πr}^{2} \frac{dh}{dt}$ .

Step by step solution

Step 1. Formula used.

The volume of the cylinder is given by the formula $V = {πr}^{2} h$ cu. units.

Step 2. Apply the differentiation.

Apply the differentiation to V with respect to t and keeping ras constant as follows.

$\frac{d}{d t} (V) = \frac{d}{d t} ({πr}^{2} h) \frac{d V}{d t} = {πr}^{2} \frac{dh}{dt}$

Step 3. Conclusion.

The derivatives $\frac{d V}{d t}$ and $\frac{d h}{d t}$ are related by $\frac{d V}{d t} = {πr}^{2} \frac{dh}{dt}$ .

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Suppose the radius r, height h, and volume V of a cylinder are functions of time t. How is $\frac{d V}{d t}$ related to $\frac{d h}{d t}$ if the radius of the cylinder is constant?

Short Answer

Step by step solution

Step 1. Formula used.

Step 2. Apply the differentiation.

Step 3. Conclusion.

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Short Answer

Step by step solution

Step 1. Formula used.

Step 2. Apply the differentiation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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Suppose the radius r, height h, and volume V of a cylinder are functions of time t. How is $\frac{d V}{d t}$ related to $\frac{d h}{d t}$ if the radius of the cylinder is constant?