The radius of a sphere is 2 in. Find the surface area of the sphere. Round to the nearest hundre

step 1 I'm going to find the surface area of this sphere. I drew it because you always want to draw wha

The radius of a sphere is 2 in. Find the surface area of the...

Key Concepts

Sphere

A sphere is a perfectly round geometrical object in three-dimensional space where every point on its surface is equidistant from its center, forming the simplest closed surface with constant curvature.

Radius

The radius is the distance from the center of a sphere to any point on its surface, serving as a key dimension in computing various properties such as the sphere's surface area and volume.

Surface Area

Surface area refers to the total area that the surface of a three-dimensional object occupies. It is a measure of how much material is needed to cover the object, and in the context of spheres, it quantifies the external curved space.

Formula for Surface Area of a Sphere

The formula for the surface area of a sphere is derived from its geometric properties and is expressed as 4?r², where r is the radius. This formula is fundamental in solving problems related to spherical surfaces.

Rounding

Rounding is the mathematical process of adjusting a numerical value to a specified degree of precision, such as the nearest hundredth, to present a more concise or appropriate level of exactness in an answer.

Transcript

00:01 I'm going to find the surface area of this sphere.

00:05 I drew it because you always want to draw whatever you have when you're doing any kind of geometry problem.

00:13 And so i drew the sphere given the parameters that i had, which were that it was a sphere, and that it has a radius of two inches.

00:22 And the second thing that you always do is write the formula that you're going to use.

00:26 So we're finding surface area.

00:27 So i wrote the surface area of a sphere formula, which is 4 pi r squared.

00:32 Now i have to figure out what the value is that i'm going to use.

00:36 So i need the radius and it just so happens that i have been given the radius value.

00:41 So i'm going to write down the value that i was given, which is two inches.

00:46 And now i'm going to substitute that into my formula.

00:49 And so i instead of r squared, i'm going to have my radius, which is two.

00:54 Now all i have to do is solve.

00:57 And so i have the surface area of my sphere.

01:00 Is 4 pi 2 squared 4 pi oh and they want this rounded to the hundreds that's come gonna come in handy later and so 2 squared is 4 and then i'm gonna do 4 i'm gonna use the commutative property here and do 4 times 4 times pi and 4 times 4 is 16 so i have 16 pie.

01:31 Now, because they want it in a round it to hundreds, i'm actually going to approximate pie to 3 .14, and i get 27...

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