Related rates Quiz

Name: ______________________   Date: __________   Score: ____ / 10

10 questions. Calculator allowed. Show your working. steplyclass.com/calculus/related-rates/quiz/

1. 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?
   1. A) 64 ft/s
   2. B) 0 ft/s
   3. C) 1.5 ft/s
   4. D) −1.5 ft/s

2. 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?

   Answer: ____________________

3. 3

   The radius of a circle grows at 2 cm/s. How fast is the area growing when the radius is 5 cm?
   1. A) 62830 cm²/s
   2. B) 62.83 cm²/s
   3. C) 628.3 cm²/s
   4. D) 6.283 cm²/s

4. 4

   The radius of a balloon grows at 1 cm/s. How fast is the volume growing when the radius is 5 cm?

   Answer: ____________________

5. 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?
   1. A) 25 ft/s
   2. B) 0 ft/s
   3. C) 72 ft/s
   4. D) 7.2 ft/s

6. 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?

   Answer: ____________________

7. 7

   The area of a circle grows at 30 cm²/s. How fast is the radius growing when the radius is 3 cm?
   1. A) 1.59 cm/s
   2. B) 1590 cm/s
   3. C) 15.9 cm/s
   4. D) 30 cm/s

8. 8

   Air is pumped into a balloon at 72 cm³/s. How fast is the radius growing when the radius is 3 cm?

   Answer: ____________________

9. 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?
   1. A) 144 ft/s
   2. B) 15 ft/s
   3. C) 1.5 ft/s
   4. D) 0 ft/s

10. 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?

    Answer: ____________________