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Volume of Hemisphere: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Volume of HemisphereVolume of Hemisphere: Definition and ExamplesTable of ContentsVolume of Hemisphere Definition of Volume of Hemisphere

A hemisphere is a three-dimensional solid figure that represents exactly half of a sphere. When a sphere is cut into two equal parts at the center, a hemisphere is formed. It consists of one flat circular base and one curved surface. The word "hemi" comes from Greek meaning "half," which accurately describes this geometric shape.

The volume of a hemisphere refers to the total capacity or space enclosed within the hemisphere. Since a hemisphere is half of a sphere, its volume formula is derived from the sphere's volume formula. The volume of a sphere is 43πr3\frac{4}{3} \pi r^334​πr3, so the volume of a hemisphere is half of that, which equals 23πr3\frac{2}{3} \pi r^332​πr3, where r is the radius of the hemisphere. This volume is measured in cubic units, such as in3in^3in3 or ft3ft^3ft3.

Examples of Volume of Hemisphere Example 1: Finding the Volume of a Hemisphere from its Diameter Problem:

The diameter of a hemisphere is 666 ft. Calculate the volume.

Step-by-step solution:

Step 1, Find what information we have. We know the diameter is 666 ft.

Step 2, Calculate the radius. The radius is half of the diameter. Radius of hemisphere=3 ft.\text{Radius of hemisphere} = 3 \text{ ft.}Radius of hemisphere=3 ft.

Step 3, Apply the volume formula for a hemisphere:

V=23πr3V = \frac{2}{3} \pi r^3V=32​πr3 V=23×3.14×33V = \frac{2}{3} \times 3.14 \times 3^3V=32​×3.14×33

Step 4, Simplify step by step:

V=23×3.14×27V = \frac{2}{3} \times 3.14 \times 27V=32​×3.14×27 V=2×3.14×9V = 2 \times 3.14 \times 9V=2×3.14×9 V=56.52 ft3V = 56.52\text{ ft}^3V=56.52 ft3

The volume of the hemisphere is 56.52 ft356.52\text{ ft}^356.52 ft3.

Example 2: Calculating Water Capacity of a Hemispherical Bowl Problem:

A hemispherical bowl has an inner radius of 444 inches. How much water can it contain?

Step-by-step solution:

Step 1, Identify what we're looking for. We need to find the volume of the hemispherical bowl, which equals how much water it can hold.

Step 2, Note the radius given: Radius of hemispherical bowl = 444 in.

Step 3, Apply the volume formula for a hemisphere:

V=23πr3V = \frac{2}{3} \pi r^3V=32​πr3 V=23×3.14×43V = \frac{2}{3} \times 3.14 \times 4^3V=32​×3.14×43

Step 4, Calculate the volume step by step:

V=23×3.14×64V = \frac{2}{3} \times 3.14 \times 64V=32​×3.14×64 V=401.923V = \frac{401.92}{3}V=3401.92​ V=133.97 in3V = 133.97\text{ in}^3V=133.97 in3

Thus, the hemispherical bowl can contain 133.97 in3133.97\text{ in}^3133.97 in3 of water.

Example 3: Finding Volume When a Sphere Is Divided Problem:

A sphere with a radius of 555 inches is divided into two equal halves. Calculate the volume of each produced hemisphere.

Step-by-step solution:

Step 1, Understand what we're looking for. We need to find the volume of each hemisphere created when the sphere is divided.

Step 2, Note that the radius of the sphere and each resulting hemisphere is the same: 5 inches.

Step 3, Apply the volume formula for a hemisphere:

V=23πr3V = \frac{2}{3} \pi r^3V=32​πr3 V=23×3.14×53V = \frac{2}{3} \times 3.14 \times 5^3V=32​×3.14×53

Step 4, Calculate the volume step by step:

V=23×3.14×125V = \frac{2}{3} \times 3.14 \times 125V=32​×3.14×125 V=7853V = \frac{785}{3}V=3785​ V=261.66 in3V = 261.66\text{ in}^3V=261.66 in3

The volume of each hemisphere is 261.66 in3261.66\text{ in}^3261.66 in3.

Comments(3)HHistoryTutorEthanNovember 6, 2025I've used this to teach my students. The clear def and examples made understanding the volume of a hemisphere a breeze. Great resource!

BBaseballPlayerNinaNovember 5, 2025I've used this to teach my students. The clear def and examples made volume of hemisphere easy for them to grasp. Thanks!

NNatureLover75September 16, 2025I used the Volume of Hemisphere explanation to help my kids understand their geometry homework. The examples with bowls made it so easy to visualize—really great resource for hands-on learning!

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