Q. 67 Recall聽that聽the聽volume,聽V,聽... [FREE SOLUTION]

Chapter 12: Q. 67 (page 945)

$Recall that the volume, V, of a cylinder is given by V (r, h) = 蟺 r^{2} h . Find \frac{鈭� V}{鈭� r} and \frac{鈭� V}{鈭� h} . What are the physical interpretations of these partial derivatives ?$

Short Answer

Expert verified

$\frac{鈭� V}{鈭� r} = 2 蟺 r h This tells us how fast the volume changes with a unit change in the radius . \frac{鈭� V}{鈭� h} = 蟺 r^{2} This tells us how fast the volume changes with a unit change in the height .$

Step by step solution

Step 1. Given information

The volume of a cylinder is given by,

V (r, h) = 蟺 r^{2} h

Step 2. Finding the partial derivatives and physical interpretation of them

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91影视

$Recall that the volume, V, of a cylinder is given by V (r, h) = 蟺 r^{2} h . Find \frac{鈭� V}{鈭� r} and \frac{鈭� V}{鈭� h} . What are the physical interpretations of these partial derivatives ?$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the partial derivatives and physical interpretation of them

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91影视

Recallthatthevolume,V,ofacylinderisgivenbyV(r,h)=蟺r2h.Find鈭�V鈭�rand鈭�V鈭�h.Whatarethephysicalinterpretationsofthesepartialderivatives?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the partial derivatives and physical interpretation of them

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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Study anywhere. Anytime. Across all devices.

$Recall that the volume, V, of a cylinder is given by V (r, h) = 蟺 r^{2} h . Find \frac{鈭� V}{鈭� r} and \frac{鈭� V}{鈭� h} . What are the physical interpretations of these partial derivatives ?$