Area Of A Sphere

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A sphere is a three-dimensional object that is round in shape. It may be characterized as a shape consisting of all points located radius away from the center. The shape of a sphere is perfectly symmetrical; it consists no edges and no vertices.


There are interesting properties of sphere that make it a unique object. For example, of all shapes that have same surface area, it is considered that the sphere gives the largest volume. Or for a given volume, you will find that the sphere is the one that possesses the smallest surface area.

Spheres appear in nature in different ways for example, water drops, planets, bubbles, and the like – this is in relation to the volume and surface area. A sphere is able to hold or contain more things in a small area compared to any other shape of the same volume.

You may also want to know that the surface area of sphere is precisely four times that of the area of a circle consisting of the same radius. This is proven by the formula of area of a circle and that of a sphere. For example, the formula of finding the area of a circle is  πr2 and that of a sphere is 4 πr2.

Having said that, let see how we calculate the area of a sphere.

The area of a sphere also referred to as the surface area is simply the number of units that cover the outside or surface of a spherical object. The equation for finding area of a sphere is:

Area = 4πr2 where r represents the radius of the sphere.

The formula for a sphere was first discovered over two thousand years ago by a Greek philosopher, mathematician, engineer, and inventor known as Archimedes of Syracus. Archimedes also found out that the surface area you find in a sphere is equal to the one (area) you get from a curved wall that is formed by its circumscribed cylinder – the smallest cylinder, which can fit or contain the sphere.

Okay, let’s now find the area of a sphere.

Let’s say that the radius of a sphere is 14 cm, how do we find the area?

Using the formula 4πr2 we can find the area

Area = 4πr2

Area = 4 x 3.14x 142

Area = 4 x 3.14 x 196

Area = 2461.76 cm2

Sometimes, you may be given the diameter of the sphere, meaning that you have to find the radius. Because we know that diameter is two times the radius, if for example, you have a diameter of 20 cm, the radius will be 10 cm. Now you can use the value for radius to find the area of the sphere.

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At other times, you may be given the surface area of a sphere and you are required to find the radius. You can use the formula to get that.

Let’s say the surface area of a sphere is 700 cm2, how do we find the radius?

Area = 4πr2

r2 = Area/4π

We rearrange the equation to find r

r = √ Area/4π

r = √700/4π

r = √700/(4×3.14)

r = √700/12.56

r = √ 55.73

r = 7.465 cm

So, the radius will be 7.465 cm.

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