4. Contextual Applications of Differentiation

Solving Related Rates Problems — Quiz

Test your understanding of solving related rates problems with 5 practice questions.

Practice Questions

Question 1

A ladder $10$ ft long leans against a wall. The bottom of the ladder slides away from the wall at $2$ ft/s. When the bottom is $6$ ft from the wall, how fast is the top of the ladder sliding down the wall?

Question 2

A spherical balloon is being inflated so that its radius increases at $0.5$ cm/s. How fast is the volume increasing when the radius is $4$ cm?

Question 3

A circular puddle has radius $3$ m and is expanding at $0.2$ m/s. How fast is its area increasing at that instant?

Question 4

A conical tank has water in it. The water height is $h$ and the water surface radius is $r$. If the cone’s shape gives a constant ratio $r:h=2:5$, which equation correctly relates $r$ and $h$ for the water?

Question 5

A balloon is a sphere with radius $r$. If the volume is increasing, which differentiated formula correctly relates $\frac{dV}{dt}$ and $\frac{dr}{dt}$?