# Circular Cylinder Calculator

## Circular Cylinder Calculator

### How to Use the Circular Cylinder Calculator

This Circular Cylinder Calculator helps you compute various properties of a cylinder, such as volume, lateral surface area, and total surface area, based on different inputs. Below are the steps and formulas for each calculation option.

#### Step 1: Choose a Calculation Type

Select the type of calculation you want to perform from the dropdown menu labeled “Choose a Calculation.” The available options are:

1. Calculate V, L, A | Given r, h
2. Calculate h, L, A | Given r, V
3. Calculate h, V, A | Given r, L
4. Calculate r, V, A | Given h, L
5. Calculate r, L, A | Given h, V
6. Calculate h, L, V | Given r, A

#### Step 2: Enter the Required Values

Based on the chosen calculation type, input the required values into the calculator. The fields that appear will correspond to the specific properties needed for that calculation.

#### Step 3: Specify the Value of Pi (π)

Input the value of π to use in the calculation. The default value is $\pi = 3.14159265359$.

#### Step 4: Choose Units and Significant Figures

Select the units for the calculated values (e.g., meters, centimeters, inches) and the number of significant figures to display in the results.

#### Step 5: Perform the Calculation

Click the “Calculate” button to perform the calculation. The results will be displayed in the result section, showing the computed values for the chosen properties.

### Examples and Formulas

Here are the examples and formulas used for each calculation type:

#### 1. Calculate V, L, A | Given r, h

Input:

• Height (h)

Formulas:

• Volume $V = \pi r^2 h$
• Lateral Surface Area $L = 2\pi rh$
• Total Surface Area $A = 2\pi r(r + h)$

Example:

• If $r = 5 \, \text{cm}$ and $h = 10 \, \text{cm}$:
• Volume $V = \pi \times 5^2 \times 10 = 785.398 \, \text{cm}^3$
• Lateral Surface Area $L = 2 \times \pi \times 5 \times 10 = 314.159 \, \text{cm}^2$
• Total Surface Area $A = 2 \times \pi \times 5 \times (5 + 10) = 471.239 \, \text{cm}^2$

#### 2. Calculate h, L, A | Given r, V

Input:

• Volume (V)

Formulas:

• Height $h = \frac{V}{\pi r^2}$
• Lateral Surface Area $L = 2\pi rh$
• Total Surface Area $A = 2\pi r(r + h)$

Example:

• If $r = 7 \, \text{cm}$ and $V = 1540 \, \text{cm}^3$:
• Height $h = \frac{1540}{\pi \times 7^2} = 10 \, \text{cm}$
• Lateral Surface Area $L = 2 \times \pi \times 7 \times 10 = 439.822 \, \text{cm}^2$
• Total Surface Area $A = 2 \times \pi \times 7 \times (7 + 10) = 748.847 \, \text{cm}^2$

#### 3. Calculate h, V, A | Given r, L

Input:

• Lateral Surface Area (L)

Formulas:

• Height $h = \frac{L}{2\pi r}$
• Volume $V = \pi r^2 h$
• Total Surface Area $A = 2\pi r(r + h)$

Example:

• If $r = 6 \, \text{cm}$ and $L = 376.991 \, \text{cm}^2$:
• Height $h = \frac{376.991}{2\pi \times 6} = 10 \, \text{cm}$
• Volume $V = \pi \times 6^2 \times 10 = 1130.973 \, \text{cm}^3$
• Total Surface Area $A = 2 \times \pi \times 6 \times (6 + 10) = 603.185 \, \text{cm}^2$

#### 4. Calculate r, V, A | Given h, L

Input:

• Height (h)
• Lateral Surface Area (L)

Formulas:

• Radius $r = \frac{L}{2\pi h}$
• Volume $V = \pi r^2 h$
• Total Surface Area $A = 2\pi r(r + h)$

Example:

• If $h = 8 \, \text{cm}$ and $L = 251.327 \, \text{cm}^2$:
• Radius $r = \frac{251.327}{2\pi \times 8} = 5 \, \text{cm}$
• Volume $V = \pi \times 5^2 \times 8 = 628.319 \, \text{cm}^3$
• Total Surface Area $A = 2 \times \pi \times 5 \times (5 + 8) = 408.407 \, \text{cm}^2$

#### 5. Calculate r, L, A | Given h, V

Input:

• Height (h)
• Volume (V)

Formulas:

• Radius $r = \sqrt{\frac{V}{\pi h}}$
• Lateral Surface Area $L = 2\pi rh$
• Total Surface Area $A = 2\pi r(r + h)$

Example:

• If $h = 9 \, \text{cm}$ and $V = 1272.345 \, \text{cm}^3$:
• Radius $r = \sqrt{\frac{1272.345}{\pi \times 9}} = 6.6667 \, \text{cm}$
• Lateral Surface Area $L = 2 \times \pi \times 6.6667 \times 9 = 377.123 \, \text{cm}^2$
• Total Surface Area $A = 2 \times \pi \times 6.6667 \times (6.6667 + 9) = 654.548 \, \text{cm}^2$

#### 6. Calculate h, L, V | Given r, A

Input:

• Total Surface Area (A)

Formulas:

• Height $h = \frac{A – 2\pi r^2}{2\pi r}$
• Volume $V = \pi r^2 h$
• Lateral Surface Area $L = 2\pi rh$

Example:

• If $r = 4 \, \text{cm}$ and $A = 251.327 \, \text{cm}^2$:
• Height $h = \frac{251.327 – 2\pi \times 4^2}{2\pi \times 4} = 5 \, \text{cm}$
• Volume $V = \pi \times 4^2 \times 5 = 251.327 \, \text{cm}^3$
• Lateral Surface Area $L = 2 \times \pi \times 4 \times 5 = 125.664 \, \text{cm}^2$

This guide covers the steps, examples, and detailed formulas for each type of calculation that the Circular Cylinder Calculator can perform.