Grade 12 Calculus: Related Rates Worksheet

Grade 12 Calculus: Related Rates

Read each problem carefully and show all your work. Remember to include units in your final answers. Use the provided space for your solutions.

A ladder 10 meters long is leaning against a vertical wall. If the bottom of the ladder is pulled away from the wall at a rate of 1 m/s, how fast is the top of the ladder sliding down the wall when the bottom is 6 meters from the wall?

Water is poured into a conical tank at a rate of 2 cubic meters per minute. The tank is 16 meters high and has a radius of 4 meters at the top. How fast is the water level rising when the water is 8 meters deep?

Determine if the following statements are true or false.

1. In related rates problems, we differentiate implicitly with respect to time.

2. If a quantity is decreasing, its rate of change with respect to time is positive.

Complete the following sentences.

1. The chain rule is essential for solving   problems.

2. Before differentiating, it is crucial to establish a   relating the variables.

A man 2 meters tall walks away from a lamppost 5 meters high at a speed of 1.5 m/s. How fast is the tip of his shadow moving when he is 10 meters from the lamppost?

Choose the best answer for the following question.

1. Which of the following is typically the first step in solving a related rates problem?