Answered: The civil engineering department has…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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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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