You may have seen objects like a soccer ball a globe or an egg, all these objects are examples of a sphere.
The surface area of the sphere can be defined as the space or region that is occupied by the surfaces of a sphere. Do not get confused between a sphere and a circle, a sphere is a three-dimensional figure whereas a circle is a two-dimensional figure.
The resultant value that you get for the surface area will always be written in square units. Mathematically, the surface area of a sphere is written as 4Πr.r where the value of Π is 3.14 or 22/7 approximately and r is regarded as the radius of the given sphere.
In this article, we will try to cover some basic concepts regarding the area of the sphere such as the formula given for it and some calculations, and try to do a brief analysis about it.
The volume of a Sphere
As mentioned above, a sphere is a geometrical shape that is three-dimensional. The literal meaning of volume is the capacity that any object can hold.
It is also defined as a scalar quantity. The volume of a sphere can be regarded as the region of space the sphere can occupy.
Mathematically, the formula given for the volume of the sphere is 4/3Πr.r.r, where the value of Π is 3.14 or 22/7 approximately and r is regarded as the radius of the given sphere.
The formula for it has been categorized into two types: volume of hollow sphere and volume of a solid sphere. In the next few sections, we shall try to solve some examples in order to understand the topic clearly.
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Some Calculations based on Surface Area of Sphere
The formula given for the surface area of the sphere is, 4Πr.r. Let us now solve some examples related to the surface area of the sphere. Some of the examples are given below:
Example 1: Find out the value of the surface area of a sphere if the radius of the sphere is 10 cm?
Solution: Given that,
The radius of the sphere = 10 cm
Using the formula of the surface area of a sphere, 4Πr.r
4 * 3.14 * 10 * 10 = 1256 cm square units.
Therefore, the surface area of a sphere for a radius of 10 cm is = 1256 cm square units.
Example 2: Find out the value of the surface area of a sphere if the radius of the sphere is 12 cm?
Solution: Given that,
The radius of the sphere = 12 cm
Using the formula of surface area of a sphere, 4Πr.r
4 * 3.14 * 10 * 10 = 1808.64 cm square units.
Therefore, the surface area of a sphere for a radius of 10 cm is = 1808.64 cm square units.
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Some Calculations based on Volume of Sphere
The formula given for the volume of the sphere is 4/3Πr.r.r where r is the radius of the sphere. Let us now solve some examples related to the volume of the sphere. Some of the examples are given below:
Example 1: Find the value of the volume of the sphere if the radius given is, 5 cm?
Solution: Given that,
The radius of the sphere is = 5 cm
Now, using the formula of volume of a sphere = 4/3Πr.r.r
4/3 * 3.14 * 5 * 5 * 5 = 510. 25 cm cubic units.
Thus, the volume of the sphere is equivalent to 510. 25 cm cubic units.
Example 2: Find the value of the volume of the sphere if the radius given is, 7 cm?
Solution: Given that,
The radius of the sphere is = 7 cm
Now, using the formula of volume of a sphere = 4/3Πr.r.r
4/3 * 3.14 * 7 * 7 * 7 = 1400.126 cm cubic units.
Thus, the volume of a sphere is equivalent to 1400.126 cm cubic units.
If you want to learn about the surface area and volume of a sphere in a detailed, fun, and interactive manner visit Cuemath.