Problem

The radius of a spherical ball is increasing at a…

01:52

Question

Answered step-by-step

Problem 6 Medium Difficulty

The radius of a sphere is increasing at a rate of $ 4 mm/s. $ How fast is the volume increasing when the diameter is $ 80 mm? $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Sam Low

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Video Transcript

mhm. In this question we're asked that given the radius of the spheres increase, we want to find how fast the volume increases at a surge in diameter. We first need to remember what the formula for the volume of the sphere is. We know that the volume of the sphere is 4/3 times pi times r cubed. But remember that the volume and the radius are both changing as functions of time. So it's more correct to write it as as functions of time. Now we'll just differentiate both sides with respect to time. Using implicit differentiation. We know that the rate of change of the volume is the prime of T equaling four thirds times pi tons. Now this are of T cubed requires a change rule. We first need to use the power rule to bring the power down. So we're going to have three times our prime times R f T squared multiplied by the derivative of R. Of T. Which is our prime of T. Yeah. And now we can plug in. Our rates were given that the volume Is increasing if the diameter is 80 That means that the radius has to be 40. Yeah. And we're also given that the rate of increase is four mm/s. So we can plug all of this information in. And also this three and three we'll cancel. So we'll have this is equal to four times pi times 40 squared times four. And when we evaluate this, we get that. This is eagle to 25,000 600 pie and this is in millimeters cubed per second. That's how you do this question.

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem

The radius of a spherical ball is increasing at a…

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals