Related Rates Worksheets
Use derivative signs and stated geometric constraints to interpret functions and rates.
Before you begin
Manipulate algebraic expressions and understand functions, limits and derivative notation.
Worked example
A spherical balloon has radius 2 cm, increasing at 5 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
- Differentiate with respect to time: dV/dt = 4πr²(dr/dt).
- Substitute the instantaneous radius and its rate of change.
Answer: 80π cm³/s
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
A spherical balloon has radius 7 cm, increasing at 1 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
2
A spherical balloon has radius 1 cm, increasing at 4 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
3
A spherical balloon has radius 8 cm, increasing at 2 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
4
A spherical balloon has radius 7 cm, increasing at 3 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
5
A spherical balloon has radius 3 cm, increasing at 1 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
6
A spherical balloon has radius 3 cm, increasing at 4 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
Answer Key
1. 196π cm³/s2. 16π cm³/s3. 512π cm³/s4. 588π cm³/s5. 36π cm³/s6. 144π cm³/s