Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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The civil engineering department has asked you to write a program to compare three different designs of water towers shown in the diagrams below.

The water towers are a cylinder topped with a half sphere. The engineers want to find the design that has the highest volume.

The dimensions of the three designs are as follows:

Design 1:
    Sphere 
        Radius 98 feet
    Cylinder
        Radius 98 feet
        Height 102 feet
        
Design 2:
    Sphere 
        Radius 90 feet
    Cylinder
        Radius 90 feet
        Height 120 feet
        
Design 3:
    Sphere 
        Radius 100 feet
    Cylinder
        Radius 100 feet
        Height 98 feet

 

Write two functions that will calculate the volume of a sphere and a cylinder respectively. Then, use these functions to write a program that will find the design with the largest volume.

Hint: Remember that the tower only consists of a half sphere.

Solve in Python Please

The formulas for the volumes of common geometric shapes are as follows:

1. **Sphere**:
   - The formula for the volume of a sphere is: 
     \[
     V = \frac{4}{3} \pi r^3
     \]
   - Here, \( V \) represents the volume, \( r \) is the radius of the sphere, and \( \pi \) (pi) is approximately 3.14159.

2. **Cylinder**:
   - The formula for the volume of a cylinder is:
     \[
     V = \pi r^2 h
     \]
   - In this formula, \( V \) stands for the volume, \( r \) refers to the radius of the base of the cylinder, \( h \) denotes the height of the cylinder, and \( \pi \) is approximately 3.14159. 

These formulas are fundamental in understanding the calculation of volumes for these three-dimensional shapes in geometry and various applications.
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Transcribed Image Text:The formulas for the volumes of common geometric shapes are as follows: 1. **Sphere**: - The formula for the volume of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] - Here, \( V \) represents the volume, \( r \) is the radius of the sphere, and \( \pi \) (pi) is approximately 3.14159. 2. **Cylinder**: - The formula for the volume of a cylinder is: \[ V = \pi r^2 h \] - In this formula, \( V \) stands for the volume, \( r \) refers to the radius of the base of the cylinder, \( h \) denotes the height of the cylinder, and \( \pi \) is approximately 3.14159. These formulas are fundamental in understanding the calculation of volumes for these three-dimensional shapes in geometry and various applications.
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