BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 36RE
To determine

Tofind:how fast the water level rises if water is 5cm deep.

Expert Solution

Answer to Problem 36RE

TheFrequency at which water level rises when the water is 5cm deep:

  0.283 cm/sec .

Explanation of Solution

Given:

Rate of change of volume (dVdt)=2cm3/s

Height is 5cm .

Radius is 3cm .

Concept used:

Volume of cone= 13πr2h .

Calculation:

  V=13πr2h .

Radius in-term of height is

  rh=310 .

  r=310h .

  V=13πr2h

Substituting the value of r in-terms of h and h itself.

  V=13π(3h10)2h .

  V=3100πh3 .

Differentiating with respect to t:

  dVdt=3100π.3h2.dhdt .

Substituting the given value.

  2=3100π.3(5)2.dhdt .

  2=9π4.dhdt

  dhdt=89π=0.283 .

Hence, Frequency at which water level rises when the wateris 5cm deep:

  0.283 cm/sec .

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!