Decimal Degrees to Degrees Minutes Seconds Calculation:
r =
Radius of the cylinder or hemisphere part of the capsule since both will be the same
a =
Length or height of the cylinder potion
Pi =
Length or height of the cylinder potion
V =
Volume of the capsule in cubic units
Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.
Decimal Degrees to Degrees Minutes Seconds Formula
The volume of a capsule can be calculated by adding the volume of a sphere and the volume of a cylinder, since the two ends of the capsule are equal to one sphere. The required inputs are the radius, it will be the same for the sphere and cylinder, and the length of the cylinder portion of the capsule. Here is the formula for a capsule made from the sphere and cylinder formulae:
V = ^{4}/_{3}PI(r)^{3} + PI(r)^{2}a
This formula can be simplified by combining the terms to the following formula, which gives the same answer:
V = PI(r)^{2}(^{4}/_{3}r + a)
Decimal Degrees to Degrees Minutes Seconds Variables
Two variables, radius and axis length, have to been known before calculating the capsule volume. The formula also uses an approximation of Pi. Variable descriptions:
Radius (r)
This is half the distance across the widest part of the cylinder perpendicular to the length of the capsule. The cylinder and sphere will have the same radius, so it is also possible to use the length from the center to the face of the sphere, or hemisphere in this case.
Axis Length (a)
This is the length of the cylinder portion of the capsule. Usually denoted with an "a" so it is not confused with the length, usually denoted "l", of the entire capsule. This is only the length of the capsule between the two hemispheres.
Pi
An approximated of Pi. Since Pi cannot be calculated exactly a value of 3.14159 is used in the calculation. You may edit this field and supply your own value if more precision is required.
Volume
Volume of the capsule is calculated by using the above formula with the supplied values. The volume result will be in cubic units. For example, if all your input measurements are in inches the resulting capsule volume will be in cubic inches.
Decimal Degrees to Degrees Minutes Seconds Solution
Let us consider the capsule with a radius of 3 and a cylinder length of 5. Here is the step-by-step solution that can be followed using the long formula:
V = ^{4}/_{3}PI(r)^{3} + PI(r)^{2}a
substitute in the known values
= ^{4}/_{3}PI(3)^{3} + PI(3)^{2}5
calculate exponents
= ^{4}/_{3}PI(27) + PI(9)5
multiply out the results
= PI(36) + PI(45)
use the approximation 3.14159 for PI
= 3.14159 * 36 + 3.14159 * 45
final multiplication
= 113.09724 + 141.37155
add the cylinder and sphere volumes
= 254.46879
The multiplication of terms is seperated into two lines in the example above so you can see the effects of Pi.
Decimal Degrees to Degrees Minutes Seconds Example
Let us try another calculation this time using real world measurements. If a tank for compressed gas has an inner radius of 5 centimeters (cm) and a cylindrical portion with an inner length of 20 cm what is the volume?
V = ^{4}/_{3}PI(r)^{3} + PI(r)^{2}a
= ^{4}/_{3}PI(5)^{3} + PI(5)^{2}20
= ^{4}/_{3}PI(125) + PI(25)20
= 523.59833 + 1570.79500
= 2094.39333
The tank will have an approximate volume of 664.96988 cm^{3}. Since Pi is not an exact value to answer is not exact, but for all practical purposes there are more decimal places than could be easily measured on a ruler.