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Hemisphere Shape: Definition and Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Hemisphere ShapeHemisphere Shape: Definition and ExamplesTable of ContentsHemisphere Shape Definition of Hemisphere Shape

A hemisphere is a geometric shape that is exactly half of a sphere, formed when a plane cuts a sphere into two equal parts. The term "hemi" means "half," and a hemisphere has specific characteristics that distinguish it from a complete sphere. It consists of a flat circular base and a curved surface, with all points on the curved surface being equidistant from the center. The radius of a hemisphere equals the radius of the sphere from which it was cut.

A hemisphere possesses unique properties that set it apart from other three-dimensional shapes. It has no edges or vertices, similar to a sphere. Since it has a circular base and one curved surface, a hemisphere is not classified as a polyhedron. The volume of a hemisphere is half that of a sphere, calculated as 23πr3\frac{2}{3} \pi r^332​πr3, while its total surface area equals 3πr23 \pi r^23πr2, which is the sum of its curved surface area (2πr22\pi r^22πr2) and the area of its circular base (πr2\pi r^2πr2).

Examples of Hemisphere Shape Example 1: Finding the Curved Surface Area of a Hemisphere Problem:

Determine the curved surface area of a hemisphere with radius 35 inches.

Step-by-step solution:

Step 1, Remember the formula for curved surface area of a hemisphere. The formula is CSA=2πr2\text{CSA} = 2\pi r^2CSA=2πr2.

Step 2, Plug in the given radius value. We know that r=35r = 35r=35 inches.

Step 3, Calculate the curved surface area using the formula.

CSA=2πr2\text{CSA} = 2\pi r^2CSA=2πr2 CSA=2×227×35×35\text{CSA} = 2 \times \frac{22}{7} \times 35 \times 35CSA=2×722​×35×35 CSA=7,700 inches2\text{CSA} = 7,700 \text{ inches}^2CSA=7,700 inches2

Step 4, State the final answer. The hemisphere with a radius of 35 inches has a curved surface area of 7,700 square inches.

Example 2: Calculating the Volume of a Hemisphere Problem:

What is the volume of a hemisphere with an 11.2 inch radius?

Step-by-step solution:

Step 1, Recall the formula for the volume of a hemisphere. The formula is Volume=23πr3\text{Volume} = \frac{2}{3} \pi r^3Volume=32​πr3.

Step 2, Insert the given radius value. We have r=11.2r = 11.2r=11.2 inches.

Step 3, Calculate the volume step by step.

Volume=23πr3\text{Volume} = \frac{2}{3} \pi r^3Volume=32​πr3 Volume=23×3.14×(11.2)3\text{Volume} = \frac{2}{3} \times 3.14 \times (11.2)^3Volume=32​×3.14×(11.2)3 Volume=23×3.14×1,404.928\text{Volume} = \frac{2}{3} \times 3.14 \times 1,404.928Volume=32​×3.14×1,404.928 Volume=2,940.98 inches3\text{Volume} = 2,940.98 \text{ inches}^3Volume=2,940.98 inches3

Step 4, Express the final answer. The volume of the hemisphere with radius 11.2 inches is 2,940.98 cubic inches.

Example 3: Finding the Capacity of a Hemispherical Bowl Problem:

Given a hemispherical bowl with a radius of 10 cm, how much water can it hold?

Step-by-step solution:

Step 1, Understand that the amount of water a bowl can hold equals its volume. For a hemispherical bowl, we'll use the formula Volume=23πr3\text{Volume} = \frac{2}{3} \pi r^3Volume=32​πr3.

Step 2, Substitute the given radius. We have r=10r = 10r=10 cm.

Step 3, Calculate the volume.

Volume=23πr3\text{Volume} = \frac{2}{3} \pi r^3Volume=32​πr3 Volume=23×3.14×(10)3\text{Volume} = \frac{2}{3} \times 3.14 \times (10)^3Volume=32​×3.14×(10)3 Volume=23×3.14×1,000\text{Volume} = \frac{2}{3} \times 3.14 \times 1,000Volume=32​×3.14×1,000 Volume=2,093.3 cubic cm\text{Volume} = 2,093.3 \text{ cubic cm}Volume=2,093.3 cubic cm

Step 4, State your answer. The hemispherical bowl with a radius of 10 cm can hold about 2,093 cubic centimeters of water.

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