Related Rates: The Draining Tank Problem

Instructions:

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question 1 of 3

You have a tank that is shaped like a prism that is on its side. The triangular base of the tank is a right triangle of height 10 m and width 10 m. See the image below. If the tank is being filled at a rate of 30 cubic meters per minute, how quickly is the height changing?

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1. Imagine you have a sheet cake with a width of 12 inches and a length of 12 inches. If you are smearing icing on it at a rate of 12 oz / minute, how quickly is the height of icing changing? One ounce is about 1 cubic inch of icing.

2. Consider a balloon that you are inflating. It is a perfect sphere. If you are inflating it at a rate of F liters per minute (dV/dt = F), what is the equation for the change in radius as a function of time?

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About This Quiz & Worksheet

The problems on this quiz are designed to test your ability to use related rates to solve draining tank problems. Your skills related to word problems will be needed to complete this quiz.

Quiz & Worksheet Goals

See if you can use your knowledge to solve draining tank problems that involve the following shapes:

  • Prisms
  • Cubes
  • Perfect spheres

Skills Practiced

This quiz and worksheet offer you the chance to use the following skills and therefore improve them:

  • Reading comprehension - ensure that you draw the most important information from the related lesson on related rates
  • Problem solving - use acquired knowledge to solve draining tank practice problems
  • Knowledge application - use your knowledge to answer questions about how parts of an equation change in relation to time

Additional Learning

If your knowledge about this topic is running a little low, you can find more information in the lesson entitled Related Rates: The Draining Tank Problem. Subject matter that is covered by this lesson includes:

  • Real-world examples of the draining tank problem
  • Using the chain rule
  • How variables change in related rate problems
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