Related rates Quiz
10 questions · easy to harder · Calculus · score and step-by-step answers
How it works
- 10 questions, about 30 minutes (a timer counts down; you can hide it). Solve it right here: no sign-up.
- 5 questions have choices. For the others you type the answer: a number like 4, −2, 7/2 or 3.5, or for example x = 4, x = 2 or x = −3, (3, 5), 2x + 1. Use ^ for powers (x^2) and sqrt for √. Any form with the same value counts (7/2 = 3.5).
- One question at a time: Back, Next, Mark for review and the question list at the bottom. A calculator is on the screen.
- At the end: your percent and grade, every question right or wrong, why a wrong choice is wrong, and its step-by-step solution. Then practise the lesson with new questions.
Your answers and results are kept in this browser only, so you can close the page and come back.
1 Question 1
A 10 ft ladder leans against a wall. The bottom slides away at 2 ft/s. How fast is the top sliding down when the bottom is 6 ft from the wall?- A) 64 ft/s
- B) 0 ft/s
- C) 1.5 ft/s
- D) −1.5 ft/s
2 Question 2
A 5 m ladder leans against a wall. The bottom slides away at 1 m/s. How fast is the top sliding down when the bottom is 3 m from the wall?Type the answer.
3 Question 3
The radius of a circle grows at 2 cm/s. How fast is the area growing when the radius is 5 cm?- A) 62830 cm²/s
- B) 62.83 cm²/s
- C) 628.3 cm²/s
- D) 6.283 cm²/s
4 Question 4
The radius of a balloon grows at 1 cm/s. How fast is the volume growing when the radius is 5 cm?Type the answer.
5 Question 5
A 13 ft ladder leans against a wall. The top slides down at 3 ft/s. How fast is the bottom sliding away when the top is 12 ft above the ground?- A) 25 ft/s
- B) 0 ft/s
- C) 72 ft/s
- D) 7.2 ft/s
6 Question 6
A 17 ft ladder leans against a wall. The bottom slides away at 2 ft/s. How fast is the top sliding down when the bottom is 8 ft from the wall?Type the answer.
7 Question 7
The area of a circle grows at 30 cm²/s. How fast is the radius growing when the radius is 3 cm?- A) 1.59 cm/s
- B) 1590 cm/s
- C) 15.9 cm/s
- D) 30 cm/s
8 Question 8
Air is pumped into a balloon at 72 cm³/s. How fast is the radius growing when the radius is 3 cm?Type the answer.
9 Question 9
A 15 ft ladder leans against a wall. The top slides down at 2 ft/s. How fast is the bottom sliding away when the top is 9 ft above the ground?- A) 144 ft/s
- B) 15 ft/s
- C) 1.5 ft/s
- D) 0 ft/s
10 Question 10
A 20 m ladder leans against a wall. The bottom slides away at 1 m/s. How fast is the top sliding down when the bottom is 16 m from the wall?Type the answer.