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How to Determine the Sphere Area and Volume?


In Geometry, a sphere is a closed three-dimensional figure, which is round in shape. Some people might get confused with the shapes “circle” and “sphere”. There is a difference between these two shapes. A circle is a two-dimensional shape where you can find the area and the perimeter. 

But, a sphere is a three-dimensional shape. You can find the volume along with the surface area. Even though both the circle and the sphere are round in shape, there exist differences in their properties. 

Let us consider two examples, wheel and a football, and we can easily get the variations. If you take an example, a wheel is an example of a circle, because it has no volume. Whereas, a football is an example of a sphere, as it has volume and the surface area.

The surface area and the volume are the two measures used for the calculation of any three-dimensional figures. The surface area for any solid is the area covered by the surface of the object, whereas the volume is the total space occupied by the object. Here, we are going to discuss how to determine the volume and the area of a sphere in a detailed way.

Let “r” be the radius of the sphere. When you take the largest possible circumference, the circumference of a sphere should be a circle. The interesting fact about a sphere is that the surface area is exactly equal to four times the area of a circle. We know that the area of a circle is πr2. Thus, the sphere surface area is,

Surface Area, S. A =  4 × πr2
Therefore, the sphere surface area is 4πr2 square units.

Now, let us discuss how to find the sphere volume. Divide the surface of the sphere into small pieces, and join the boundaries to the centre of the sphere. Now, you can get the number of square pyramids. We know that the volume of the pyramid is one-third of the area of the base times the height. When you add all the pyramids together, you have one-third of the surface area of the sphere times the radius. It can be written as:

V = (⅓) (4πr2) × r

Thus, the volume of the cone is (4/3)πr3 Cubic units.
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