# Capsule Calculator

Contents

### Steps to Use the Calculator

1. Choose a Calculation:

• Begin by selecting the type of calculation you wish to perform from the dropdown menu labeled “Choose a Calculation.”
• The available options are:
• Find V, S, C | Given r, a: Calculate Volume (V), Surface Area (S), and Circumference (C) given the radius (r) and side length (a).
• Find a, S, C | Given r, V: Calculate Side Length (a), Surface Area (S), and Circumference (C) given the radius (r) and Volume (V).
• Find a, V, C | Given r, S: Calculate Side Length (a), Volume (V), and Circumference (C) given the radius (r) and Surface Area (S).
• Find r, V, S | Given a, C: Calculate Radius (r), Volume (V), and Surface Area (S) given the side length (a) and Circumference (C).
2. Enter the Required Values:

• Based on your selection, input the necessary values in the fields provided.
• For example, if you choose “Find V, S, C | Given r, a,” you will need to enter the radius (r) and side length (a).
• The input fields will change dynamically according to your selection.
3. Set the Value of π (Pi):

• Enter the value of π (pi) to be used in calculations. The default value is 3.14159265359, suitable for most calculations.
4. Choose Units:

• Select the units for your calculations (e.g., meters, centimeters, inches). If you do not want to specify units, you can leave this as “none.”
5. Select Significant Figures:

• Choose the number of significant figures to display in the results. The default is 6 significant figures, but you can adjust this based on your preference.
6. Perform the Calculation:

• Click the Calculate button to perform the calculations. The calculator will display the computed values based on the inputs and selected calculation type.
7. Review the Results:

• The results will appear below the calculation button, showing the relevant values based on your inputs and selected calculation type.
8. Resetting the Calculator:

• To reset all fields and start a new calculation, click the Clear button.

### Formulas Used

1. Find V, S, C | Given r, a

• Volume (V):
$V=\pi {r}^{2}\left(\frac{4}{3}r+a\right)$

• Surface Area (S):
$S=2\pi r\left(2r+a\right)$

• Circumference (C):
$C=2\pi r$

2. Find a, S, C | Given r, V

• Side Length (a):
$a=\frac{V}{\pi {r}^{2}}-\frac{4}{3}r$

• Surface Area (S):
$S=2\pi r\left(2r+a\right)$

• Circumference (C):
$C=2\pi r$

3. Find a, V, C | Given r, S

• Side Length (a):
$a=\frac{S}{2\pi r}-2r$

• Volume (V):
$V=\pi {r}^{2}\left(\frac{4}{3}r+a\right)$

• Circumference (C):
$C=2\pi r$

4. Find r, V, S | Given a, C

$r=\frac{C}{2\pi }$

• Volume (V):
$V=\pi {r}^{2}\left(\frac{4}{3}r+a\right)$

• Surface Area (S):
$S=2\pi r\left(2r+a\right)$

### Examples

Example 1: Calculate Volume, Surface Area, and Circumference Given Radius and Side Length

• Calculation Type: Find V, S, C | Given r, a
• Inputs:
• Radius (r) = 5 cm
• Side Length (a) = 10 cm
• π (pi) = 3.14159265359
• Units = cm
• Results:
• Volume (V) = 1047.197551 cm³
• Surface Area (S) = 471.238898 cm²
• Circumference (C) = 31.415927 cm

Example 2: Calculate Side Length, Surface Area, and Circumference Given Radius and Volume

• Calculation Type: Find a, S, C | Given r, V
• Inputs:
• Radius (r) = 4 m
• Volume (V) = 500 m³
• π (pi) = 3.14159265359
• Units = m
• Results:
• Side Length (a) = 8.322678 m
• Surface Area (S) = 402.123860 m²
• Circumference (C) = 25.132741 m