19. Emptying a tank A vertical right-circular cylindrical tank mea- sures 30 ft high and 20 ft in diameter. It is full of kerosene weigh- ing 51.2 Ib/ft. How much work does it take to pump the kerosene to the level of the top of the tank?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Problem 19. Emptying a Tank

**Question:**
A vertical right-circular cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb/ft³. How much work does it take to pump the kerosene to the level of the top of the tank?

**Explanation:**
The problem involves calculating the work required to pump kerosene from a cylindrical tank. Here are the details:

- The tank is a vertical right-circular cylinder.
- Height of the tank: 30 feet.
- Diameter of the tank: 20 feet.
- Weight density of the kerosene: 51.2 pounds per cubic foot.

**Diagrams or Graphs:**
There are no diagrams or graphs provided in the problem.

**Computational Approach:**
To solve this, you would typically:

1. Calculate the volume of the kerosene in a small strip at height \(y\) with thickness \(dy\).
2. Find the weight of the kerosene in that strip.
3. Determine the distance this strip needs to be pumped to the top of the tank.
4. Multiply the weight by the distance to get the work done for that strip.
5. Integrate this over the entire height of the tank from \(y = 0\) to \(y = 30\) feet.

This ensures you calculate the total work needed to pump all the kerosene to the top of the tank.
Transcribed Image Text:### Problem 19. Emptying a Tank **Question:** A vertical right-circular cylindrical tank measures 30 ft high and 20 ft in diameter. It is full of kerosene weighing 51.2 lb/ft³. How much work does it take to pump the kerosene to the level of the top of the tank? **Explanation:** The problem involves calculating the work required to pump kerosene from a cylindrical tank. Here are the details: - The tank is a vertical right-circular cylinder. - Height of the tank: 30 feet. - Diameter of the tank: 20 feet. - Weight density of the kerosene: 51.2 pounds per cubic foot. **Diagrams or Graphs:** There are no diagrams or graphs provided in the problem. **Computational Approach:** To solve this, you would typically: 1. Calculate the volume of the kerosene in a small strip at height \(y\) with thickness \(dy\). 2. Find the weight of the kerosene in that strip. 3. Determine the distance this strip needs to be pumped to the top of the tank. 4. Multiply the weight by the distance to get the work done for that strip. 5. Integrate this over the entire height of the tank from \(y = 0\) to \(y = 30\) feet. This ensures you calculate the total work needed to pump all the kerosene to the top of the tank.
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