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Related Rates - Worksheet 2 - 12th Grade

Easy

Use derivative signs and stated geometric constraints to interpret functions and rates.

easy: Start with the preview and follow the worked example.

10 problems · 30-35 minutes · Skills: derivatives, related rates, calculus

About This Worksheet

This easy-level worksheet contains 10 problems designed for 12th Grade students practicing related rates. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

  • Use derivative signs and stated geometric constraints to interpret functions and rates.
  • Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: 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.
Solution Steps:
  1. Differentiate with respect to time: dV/dt = 4πr²(dr/dt).
  2. Substitute the instantaneous radius and its rate of change.
Answer: 80π cm³/s
Tip: Check your result using the method in the example before moving to the next question.
1
A spherical balloon has radius 7 cm, increasing at 4 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
2
A spherical balloon has radius 5 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 3 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
4
A spherical balloon has radius 9 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 4 cm, increasing at 2 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
6
A spherical balloon has radius 1 cm, increasing at 2 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
7
A spherical balloon has radius 6 cm, increasing at 4 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
8
A spherical balloon has radius 7 cm, increasing at 5 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
9
A spherical balloon has radius 9 cm, increasing at 2 cm/s. Find dV/dt at this instant. Use V = (4/3)πr³ and leave π exact.
10
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.

Answer Key

1. 784π cm³/s2. 400π cm³/s3. 768π cm³/s4. 972π cm³/s5. 128π cm³/s6. 8π cm³/s7. 576π cm³/s8. 980π cm³/s9. 648π cm³/s10. 16π cm³/s

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What skills does this applications of derivatives worksheet cover?

This worksheet focuses on derivatives, related rates, calculus. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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How many problems are on this worksheet?

This worksheet contains 10 problems. It typically takes 30-35 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.