Hemisphere Volume Calculator

Diameter

Diameter (cm): Diameter (in): Diameter (ft): Diameter (m):

Volume

Volume (cm³): Volume (in³): Volume (ft³): Volume (m³): Volume (L):

Surface Areas

Base Surface Area (cm²): Base Surface Area (in²): Base Surface Area (ft²): Base Surface Area (m²): Cap Surface Area (cm²): Cap Surface Area (in²): Cap Surface Area (ft²): Cap Surface Area (m²): Total Surface Area (cm²): Total Surface Area (in²): Total Surface Area (ft²): Total Surface Area (m²):

Surface to Volume Ratio

Surface to Volume Ratio (cm⁻¹): Surface to Volume Ratio (in⁻¹): Surface to Volume Ratio (m⁻¹):

1. What is a Hemisphere Volume Calculator?

Definition: This calculator computes the volume, diameter, surface areas (base, cap, total), and surface to volume ratio of a hemisphere based on its diameter.

Purpose: Useful in geometry and engineering for analyzing hemispherical shapes (e.g., domes, bowls).

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ d = 2r \] \[ V = \frac{2}{3} \pi r^3 \] \[ A_b = \pi r^2 \] \[ A_c = 2 \pi r^2 \] \[ A = 3 \pi r^2 \] \[ \frac{A}{V} = \frac{9}{2r} \]

Unit Conversions:

Input (Length): cm (×1), m (×100), ft (×30.48), in (×2.54)
Output (Length): cm (direct), in (×0.393701), ft (×0.0328084), m (×0.01)
Output (Area): cm² (direct), in² (×0.155), ft² (×0.00107639), m² (×0.0001)
Output (Volume): cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001), L (×0.001)
Output (SVR): cm⁻¹ (direct), in⁻¹ (×0.393701), ft⁻¹ (×0.0328084), m⁻¹ (×0.01)

Explanation: The diameter is converted to cm, the radius is derived, and all properties are calculated and converted to multiple units.

3. Importance of Hemisphere Volume Calculation

Details: Hemisphere volume calculations are essential in architecture (e.g., designing domes), engineering (e.g., storage tanks), and physics for understanding spherical properties.

4. Using the Calculator

Tips: Enter the diameter \( d \) in cm, m, ft, or in (must be >0). Results show the diameter, volume, surface areas (base, cap, total), and surface to volume ratio in cm, in, ft, m, and L (for volume).

FAQs

What is a hemisphere?

A hemisphere is half of a sphere, derived from the Greek "hemi" (half) and Latin "shaera" (globe). It is commonly used to describe divisions of the Earth, such as northern/southern or eastern/western hemispheres.

How do I calculate the volume of a hemisphere?

To calculate the volume of a hemisphere given its radius \( r \), use the formula \( V = \frac{2}{3} \pi r^3 \). Alternatively, if you know the diameter \( d \), cube the diameter, multiply by \(\pi\), and divide by 12 (\( V = \frac{\pi d^3}{12} \)).

How do I calculate the surface area of a hemisphere?

To calculate the surface area of a hemisphere, square the radius \( r \), multiply by \(\pi\), and then multiply by 3. Mathematically, this is \( A = 3 \pi r^2 \).

How many faces are on a hemisphere?

A hemisphere has 1 face, which is the flat base. The dome part is classified as a curved surface. It also has 1 circular edge and 0 vertices.

How do I calculate the volume of a hemisphere given its diameter?

To calculate the volume of a hemisphere given its diameter \( d \), cube the diameter, multiply by \(\pi\), and divide by 12. The formula is \( V = \frac{\pi d^3}{12} \).

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