13. a) Find the work done if the tank shown below is full of water and all of the water must be pumped out of the spout. I m 3m b) Find the work done if the tank shown below is half full of oil that has density 900 kg/m² that must be pumped out of the spout

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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Please show me how to get to the answer.

**Options:**

a) \( 1,411,200\pi \, \text{J} \)  
b) \( 2,556,141.15 \, \text{J} \)  

*Note: \( \pi \) represents the mathematical constant Pi, approximately equal to 3.14159, often used in calculations involving circles or periodic functions.*
Transcribed Image Text:**Options:** a) \( 1,411,200\pi \, \text{J} \) b) \( 2,556,141.15 \, \text{J} \) *Note: \( \pi \) represents the mathematical constant Pi, approximately equal to 3.14159, often used in calculations involving circles or periodic functions.*
**Problem 13**

a) Calculate the work done when the tank, as illustrated below, is completely filled with water and all the water must be pumped out through the spout.

**Description of the Diagram:**
A diagram of a spherical tank is shown. The radius of the tank is 3 meters. There is a spout at the top which is 1 meter above the tank.

b) Calculate the work done when the same tank is half full of oil. The oil has a density of \(900 \, \text{kg/m}^3\) and must be pumped out through the spout.

**Notes:**
For both parts, consider using the formula for work done in pumping liquids, which involves calculating the force necessary to move the fluid a certain distance.
Transcribed Image Text:**Problem 13** a) Calculate the work done when the tank, as illustrated below, is completely filled with water and all the water must be pumped out through the spout. **Description of the Diagram:** A diagram of a spherical tank is shown. The radius of the tank is 3 meters. There is a spout at the top which is 1 meter above the tank. b) Calculate the work done when the same tank is half full of oil. The oil has a density of \(900 \, \text{kg/m}^3\) and must be pumped out through the spout. **Notes:** For both parts, consider using the formula for work done in pumping liquids, which involves calculating the force necessary to move the fluid a certain distance.
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