Capsule Calculator

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

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

   • 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):
     $$S=2\pi r(2r+a)$$

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

   • Circumference (C):
     $$C=2\pi r$$

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

   • Radius (r):
     $$r=\frac{C}{2\pi }$$

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

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

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