When building software for engineers, architects, or machinists, you quickly learn one golden rule: nobody uses meters on the shop floor or construction site. Everything is measured in millimeters (mm).
Today, we will build a practical C++ console application that estimates the mass of various 3D structural shapes based on their material density and dimensions—optimized for real-world blueprints.
📐 The Physics & Math Behind It
The core formula is straightforward:
Mass = Density × Volume
Since density is typically given in kg/m³ and structural dimensions are in mm, our calculated volume will initially be in cubic millimeters (mm³). To get the correct mass in kilograms, we must divide the final volume by 1,000,000,000 (10⁹) to convert mm³ to m³.
Here are the geometric shapes we will support:
Rectangular Prism: V = l × w × h
Solid Cylinder: V = (π × d² × l) / 4
Hollow Tube: V = [π × (D² - d²) × l] / 4
Hexagonal Prism: V = (3 × √3 / 2) × a² × l
#include <iostream>
#include <cmath>
using namespace std;
int main()
{
char solid;
double mat_density;
double mass = 0.0;
cout << "Enter the solid type: r(rectangular prism), c(cylinder), t(tube), h(hexagonal prism): ";
cin >> solid;
while (solid != 'r' && solid != 'c' && solid != 't' && solid != 'h') {
cout << "Invalid solid type! Enter r, c, t, or h: ";
cin >> solid;
}
cout << "Enter the material density [kg/m3]: ";
cin >> mat_density;
switch(solid){
case 'r': {
double l, w, h;
cout << "Enter the length of the prism [mm]: ";
cin >> l;
cout << "Enter the width of the prism [mm]: ";
cin >> h;
cout << "Enter the height of the prism [mm]: ";
cin >> w;
mass = mat_density * (l * w * h) / 1000000000.0;
break;
}
case 'c': {
double d, l;
cout << "Enter the length of the cylinder [mm]: ";
cin >> l;
cout << "Enter the diameter of the base [mm]: ";
cin >> d;
mass = mat_density * M_PI * d * d * l / 4.0 / 1000000000.0;
break;
}
case 't': {
double D, d, l;
cout << "Enter the length of the tube [mm]: ";
cin >> l;
cout << "Enter the outer diameter [mm]: ";
cin >> D;
cout << "Enter the inner diameter [mm]: ";
cin >> d;
if (D <= d) {
cout << "[Error] Outer diameter must be larger than inner diameter!\n";
return 0;
}
mass = mat_density * l * M_PI * (D * D - d * d) / 4.0 / 1000000000.0;
break;
}
case 'h': {
double a, l;
cout << "Enter the length of the prism [mm]: ";
cin >> l;
cout << "Enter the side of the base [mm]: ";
cin >> a;
mass = mat_density * (3.0 * sqrt(3.0) / 2.0) * a * a * l / 1000000000.0;
break;
}
}
cout << "The mass of the solid is: " << mass << " kg" << endl;
return 0;
}
⚡ Key Takeaways for Clean Code
Hardcoded Constants over pow(): Using 1000000000.0 directly instead of pow(10, 9) avoids runtime floating-point overhead, making compile-time math cleaner.
Early Returns: Catching the impossible case where a pipe's inner diameter is larger than its outer diameter prevents negative mass artifacts.
Initialization Safeguards: Forcing mass = 0.0 at the top ensures that if something catastrophic happens, your system won't output garbage data stored in your RAM.
What shape should we add next? Steel I-beams or asymmetric channels? Let me know in the comments!
