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How to Find the Volume of a Half Sphere

how to find volume of half sphere: 3D sphere in half

Understanding how to find the volume of a half sphere, or in other words, the volume of a hemisphere, is easier than it seems. Keep in mind that volume is the amount of space that a three-dimensional shape takes up, whereas the surface area is the total area of all the surfaces of that three-dimensional shape.

First, we need to review the formula for the volume of the sphere. The volume formula for a sphere is (4𝛑r²)/3, where r stands for the radius of the sphere. (The radius is the distance from the center of the sphere).

Volume of a Sphere and Hemisphere

how to find volume of half sphere: sphere infographic

Keep in mind that volume is measured in cubic units. Hemi means half, so the volume of half of a sphere (hemisphere) is just half the volume V of a sphere.

Let's say you have a model globe with a radius r. The radius of the hemisphere is the same as the radius of the sphere. We see that the volume formula for the sphere, (4𝛑r²)/3, is exactly two times the hemisphere formula, (2𝛑r²)/3. Here’s how these formulas work out:

how to find volume of half sphere: formula for getting the volume of a sphere and a hemisphere

Surface Area of a Sphere and Hemisphere

To find the surface area of a sphere, you can’t just multiply the surface area of a hemisphere by two.

Just like before, the radius of a hemisphere is exactly the same as the radius of a sphere. However, when we compare the formula total surface area of a sphere to the surface area formula for a hemisphere, we see that we need to take into account the flat part of the hemisphere. Unlike the volume of a half sphere, the surface area of a half sphere is not exactly half that of the surface area of a sphere.

formula of the surface area of a hemisphere

How to Find the Volume of Half Spheres vs. Surface Area

The volume of a half sphere is its full amount of space in terms of cubic units. The surface area of a half sphere is the total outward surface measured in square units. All you need to remember is:

The volume of the hemisphere is exactly half the volume of a sphere:

volume of a hemisphere formula

The surface area of a hemisphere has its own formula and is slightly more than half the surface area of a sphere:

surface area of a hemisphere formula

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