Here are some most common formulae based mathematical programs. These programming test is basically for checking the mathematical knowledge and Java operator precedence to implement these formulae.

- Program to calculate the area of rectangle

**Input:**Width = 10; Height = 5

**Output:**

Area of Rectangle = Width * Height

= 10 * 5

= 50 - Program to calculate the volume of sphere

**Input:**Radius = 48; Pie = 3.14

**Output:**

Volume = (4.0/3.0) * pie * (radius * radius * radius);

= (4.0/3.0) * 3.14 * 48 * 48 * 48

= 463433.132812 - Program find the area of the pentagon

**Input:**s = 13; a = 5;

**Output:**

Area of Pentagon = (5.0/2.0) * s * a

= (5.0/2.0) * 13 * 5

= 162.5 - Program to find the area of parallelogram

**Input:**base = 4; height = 18;

**Output:**

Area of Parallelogram = base * height;

= 4 * 18

= 72 - Program to find the area of square

**Input:**a = 13

**Output:**

Area of Square = a2

= 132

= 169 - Program to find the surface area of sphere

**Input:**Radius = 37, Pie = 3.14

**Output:**

Volume = 4 * pie * (radius * radius);

= 4 * 3.14 * 37 * 37

= 17210.285714 - Program to find the volume of cone

**Input:**Radius = 38, Height = 35, Pie = 3.14

**Output:**

Volume = pie * radius * radius * height/3;

= 3.14 * 38 * 38 * 35/3

= 48766.666667 - Program to find the volume of the cube

**Input:**side = 4

**Output:**

Volume of cube = side3

= 43

= 64 - Program to find the volume of cylinder

**Input:**radius (r) = 38 , height (h) = 35

**Output:**

Volume of the cylinder = pie * radius2 * height

= 3.14 * 38* 38 * 35

= 146300.000000 - Program to calculate the CGPA percentage

CGPA percentage is = (float)(9.5 * (CGPA));

**Input:**

CGPA = (Grades in all Subjects) / (Total Number of Subjects).

English = 9.1;

Hindi = 8.5;

Maths = 9.5;

Science =9.6;

SocialStudy = 8.6;

CGPA = (9.1+8.5+9.5+9.6+8.6)/(5.0);

**Output:**CGPA percentage is = 86.070000 - Program to convert Celsius into Fahrenheit

Temperature in Fahrenheit = ((celsius * 9) / 5) + 32

**Input:**celsius= 12

**Output:**Temperature in Fahrenheit = 53.6 - Program to convert days into years

**Input:**days= 799;

**Output:**

Number of years = days / 365;

= 799 / 365

= 2 - Program to convert Fahrenheit into Celsius

Temperature in Celsius = ((Fahrenheit-32)*5)/9

**Input:**Fahrenheit = 54

**Output:**Temperature in Celsius= ((54-32)*5)/9 = 12.22222 - Program to find the area of an equilateral triangle

**Input:**side (a) = 5

**Output:**

Area of Equilateral Triangle = ( 1.73 * a * a) / 4

= ( 1.73 * 5 * 5) / 4

= 10.81250 - Program to find the area of a triangle

**Input:**b = 5; h = 12

**Output:**Area of Triangle = (b * h) / 2

= (5 * 12) / 2

= 30.0 - Program to find the area of the right angle triangle

**Input:**b = 5; h = 8

**Output:**Area of Triangle = (b * h) / 2

= (5 * 8) / 2

= 20.0 - Program to find the perimeter of the rectangle

**Input:**a = c = 5

b = d = 4

**Output:**Perimeter of Rectangle = 2 * ( a + b);

= 2 * (5 + 4)

= 18.00000 - Program to find the simple interest

Simple Interest = (P × R × T) / 100

**Input:**P = 34000, R = 30,T = 5

where P = Principal Amount, R = Rate per Annum, T = Time (years)

**Output:**Simple Interest = 51000.000 - Program to find the surface area of a cube

Surface Area Of Cube = 6 ( a * a )

**Input:**b = 5, h = 5

a (side) = length = breadth = height

**Output:**Surface Area Of Cube = 6 * 5 * 5=150.00000 - Program to find the surface area of sphere

**Input:**l= 2, w = 3, h = 5;

where l = length, w = width and h = height.

**Output:**

Surface Area OfCuboid = 2 * (l * w+ w * h + h * l)

= 2 * (2 * 3 + 3 * 5 + 5 * 2)

= 62.00000 - Program to find the surface area of the cylinder

Surface Area of Cylinder = 2 Π (r + h)

**Input:**r = 2.0, h = 5.0

**Output:**

Surface Area of Cylinder = 2 Π (r + h)

Here, r = radius, h = height, and Π ( pie ) = 3.14

= 2 * 3.14 * ( 2.0 + 5.0)

= 44.00000 - Write a Java program to compute the area of a hexagon.

Area of a hexagon = (6 * s^2)/(4*tan(π/6))

where s is the length of a side

**Input:**Input the length of a side of the hexagon: 6

**Output:**The area of the hexagon is: 93.53074360871938 - Write a Java program to compute the area of a polygon.

Area of a polygon = (n*s^2)/(4*tan(π/n))

where n is n-sided polygon and s is the length of a side

**Input:**

Input the number of sides on the polygon: 7

Input the length of one of the sides: 6

**Output:**The area is: 130.82084798405722 - Write a Java program to compute the distance between two points on the surface of earth.

Distance between the two points [ (x1,y1) & (x2,y2)]

d = radius * arccos(sin(x1) * sin(x2) + cos(x1) * cos(x2) * cos(y1 – y2))

Radius of the earth r = 6371.01 Kilometers

**Input:**

Input the latitude of coordinate 1: 25

Input the longitude of coordinate 1: 35

Input the latitude of coordinate 2: 35.5

Input the longitude of coordinate 2: 25.5

**Output:**The distance between those points is: 1480.0848451069087 km