Instrumentation & Automation
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Application for Windows ⁄ Android

Area and volume of geometric shapes

In practical calculations of specialists in industrial automation, as well as in the design of automated control systems for technological processes, it is often required to calculate the surface area, and the volume of various geometric shapes.

These calculations are implemented in the Android application "Instrumentation & Automation". Below are the formulas by which the program calculates the area and volume of geometric shapes.

Table 1.

Calculating the lengths and areas of plane figures
S - arean - number of sides of a regular polygon
p - semiperimeterr - radius of inscribed circle
P - perimeterR - radius of the circumscribed circle
h - heightα - angle in radians
C - circumferenceβ - angle in degrees
l - arc length
Triangle
Formulas for calculating the area of a triangle S = (b h) / 2;
S = (a b c) / (4 R);
S = p r;
S = √(p(p-a)(p-b)(p-c));
p = (a + b + c) / 2;
Parallelogram
Formulas for calculating the area of a parallelogram S = b h;
Rhombus
Formulas for calculating the area of a rhombus S = (D d) / 2;
Rectangle
Formulas for calculating the area of a rectangle S = a b;
S = a√(d2 - a2);
S = b√(d2 - b2);
d = √(a2 + b2);
Trapezium
Formulas for calculating the area of a trapezium S = ((a + b) / 2) h;
Regular polygon
Formulas for calculating the area of a regular polygon Sn = (n an r) / 2;
Sn = ((n an) / 2) √(R2 - (r2 / 4));
Pn = 2 n R Sin(π / n);
Circle
Formulas for calculating the area of a circle S = π r2;
S = (π d2) / 4;
C = 2 π r;
C = π d;
Sector
Formulas for calculating the area of a sector l = α r;
S = (r2 α) / 2;
l = (π r β) / 180;
S = (π r2 β) / 360;
Segment
Formulas for calculating the area of a segment c = 2 √(h (2 r - h));
S = ½ (r l - c (r - h));
Ring
Formulas for calculating the area of a ring S = π (R2 - r2);
Ring sector
Formulas for calculating the area of a ring sector S = α (R2 - r2) / 2;
S = β π (R2 - r2) / 360;
Ellipse
Formulas for calculating the area of an ellipse S = π a b;
Calculation of areas of surfaces and volumes of geometric bodies
S - surface arear - radius of a circle
Ssid - side surface areaR - ball radius
Sbs - base areaD - ball diameter
Pbs - base perimeterH - height
V - volumea - apothem
l - generatrix
Rectangular parallelepiped
The volume of a rectangular parallelepiped S = 2 (ab + bc + ac);
V = a b c;
Cube
The volume of the cube S = 6 a2;
V = a3;
Regular pyramid
The volume of the regular pyramid Ssid = ½ Pbs a;
V = (Sbs H) / 3;
Regular truncated pyramid
The volume of a regular truncated pyramid Ssid = ½ (Pbs1 + Pbs2) a;
V = H (Sbs1+Sbs2 + √(Sbs1Sbs2)) / 3;
Cylinder
The volume of the cylinder Ssid = 2 π r H;
S = 2 π r H + 2 π r2;
V = π r2 H;
Hollow cylinder
The volume of the hollow cylinder Ssid = 2 π H (r1 + r2);
V = π H (r22 - r12),
r2 > r1;
Cone
The volume of the cone Ssid = π r l;
Ssid = π r √(r2 + H2);
V = (π r2 H) / 3;
Truncated cone
The volume of the truncated cone Ssid = π l (r1 + r2);
V = π H (r12 + r22 + r1 r2) / 3;
Ball
The volume of a ball S = 4 π R2;
S = π D2;
V = 4 π R3 / 3;
V = π D3 / 6;
Spherical sector
The volume of the spherical sector Ssid = π R (r + 2H);
V = (2 π R2 H) / 3;
Spherical segment
The volume of a spherical segment Ssid = 2 π R H;
V = (π H (3 r2 + H2)) / 6;
V = (π H2 (3 R - H)) / 3;