The Hemisphere Calculator on your website is a tool that allows users to perform geometric calculations related to hemispheres. By inputting the radius of a hemisphere, the calculator computes three important properties of the hemisphere:

   The volume of a hemisphere is the space it occupies. Given the radius r, the formula for calculating the volume of a hemisphere is:

   V = 23πr^3

   This formula derives from the volume of a full sphere 43πr^3, and since a hemisphere is half of a sphere, we take half of that value.

2. Curved Surface Area of Hemisphere: 

   The curved surface area refers to the area of the "dome" portion of the hemisphere, excluding the flat circular base. The formula for the curved surface area A_curved is:

   A_curved = 2πr^2

   This formula represents the surface area of the spherical part of the hemisphere.

3. Total Surface Area of Hemisphere: 

   The total surface area includes both the curved surface area and the area of the flat circular base. The total surface area A_total is given by:

   A_total = 3πr^2

   This accounts for the curved surface area (as described above) plus the area of the circular baseπr^2.

1. Input: Users provide the radius of the hemisphere as input.

2. Calculation: Based on the input radius, the calculator uses the above formulas to compute:

   - Volume

   - Curved Surface Area

   - Total Surface Area

3. Output: The calculator displays the calculated values for the Volume, Curved Surface Area, and Total Surface Area, providing users with a clear understanding of the hemisphere's dimensions.

For a hemisphere with a radius of 5 units:

- Volume: 23π(5^3) ≈ 261.8

- Curved Surface Area: 2π(5^2) = 157.1

- Total Surface Area: 3π(5^2) = 235.6

This calculator is helpful for anyone needing to quickly calculate the geometric properties of a hemisphere, especially in fields like physics, engineering, and architecture.