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Geometry for Kids6 chapters | 45 lessons

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Instructor:
*Nola Bridgens*

Nola has taught elementary school and tutored for four years. She has a bachelor's degree in Elementary Education, a master's degree in Marketing, and is a certified teacher.

In this lesson, we will discuss the elements of a hemisphere and define surface area. We will also learn the formula to calculate the surface area of a hemisphere and how to apply it.

Have you ever heard the terms, 'Northern and Southern Hemispheres', when referring to the Earth? A **hemisphere** is precisely half of a sphere, which is a perfectly round 3-dimensional object, such as a ball. Imagine cutting one of your own balls straight through the middle, which would give you a hemisphere, as shown in this image.

**Surface area** is the sum of all the sides of a 3-dimensional object. In the case of a sphere, think about an orange. If you were to peel an orange, its surface area would be the total amount of the peel. The surface area of a hemisphere would be like the peel of half of the orange.

Before we learn the formula for the surface area of a hemisphere, we need to review the elements of a hemisphere:

- The radius is a line that connects the center point of a circle or sphere with the outside layer, or
**circumference**. - The diameter is twice the radius or distance from one side of the circumference to the other through the center point.
- TT is the symbol we use for
*pie*and it represents the ratio of the circumference of a circle to its diameter. TT always equals 3.14.

As long as you know the radius of a hemisphere, the formula we use to calculate its surface area is very straightforward.

Let's try an example: find the surface area of a hemisphere with a radius of 5 inches.

2TTr2 = (2)(3.14)(52) = (6.28)(52) = (6.28)(25) = 157 square inches.

A hemisphere with a radius of 5 inches has a surface area of 157 square inches.

But what if we only know the diameter of the hemisphere? Well, we know that the diameter is equal to two times the radius. So, we can divide the diameter by 2 to find the radius.

Let's try another example: find the surface area of a hemisphere with a diameter of 8 feet.

The diameter is 8, and we need to know the radius. Here, 8 / 2 = 4, so the radius is 4. Let's plug this number into our formula:

2TTr2 = (2)(3.14)(42) = (6.28)(42) = (6.28)(16) = 100.48 square feet.

A hemisphere with a diameter of 8 feet has a surface area of 100.48 square feet.

How about if we wrap up this lesson with one more example: find the surface area of a hemisphere with a diameter of 4 feet. You need to know the radius for the surface area formula, so you divide 4 by 2 and find that the radius is 2 feet. Now you are ready to plug this information into the formula:

2TTr2 = (2)(3.14)(22) = (6.28)(22) = (6.28)(4) = 25.12 square feet.

In this lesson, we learned that half of a sphere is called a **hemisphere**, and its **surface area** is the entire outside layer, or the **circumference**. The formula for the surface area of a hemisphere is 2TTr2.

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Geometry for Kids6 chapters | 45 lessons

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