All the shapes occupy a definite shape. It becomes crucial many times to calculate the area of different shapes. Both two-dimensional, as well as three-dimensional shapes, have a definite area. Two of the most common three-dimensional shapes are cones and spheres of which we all are familiar. From a football which is a sphere in shape to an ice-cream cone. We can easily observe these shapes all around. Thus it becomes necessary to have knowledge regarding these shapes. We will be discussing ways of calculating the surface area of cone and sphere in detail.
Cone
It is a three-dimensional shape with a vertex. One can imagine it as many triangles rotated around a fixed axis. A cone has a flat base, thus it consists of two types of surface area and they are the total surface area that includes the base of the cone in it whereas the other one is the curved surface area of the cone, area of the base is excluded while calculating curved surface area of the cone. Let us look at both the formulas used to calculate them.
The surface area of a cone:
Let us take l as the slant height and r as the radius of the base of the cone. Now let us first look at the formula to calculate the total surface area of the cone. It is given by πr(r + l), where π is the constant, r is the given radius and l is the slant height of the cone. One will understand the formula better if one looks at it after opening the bracket. πr2 + πrl will be the formula after removing the bracket. We can see that there is an expression πr2, and we all know that is the same formula used for calculating the area of a circle. Thus we are adding the area of the base that is circular and the area of the remaining part. One must have got it, that to calculate the curved surface area of the cone we just have to subtract the area of the base from the total surface area. Thus we will get to the expression for the curved surface area as πrl.
Sphere:
A unique but common shape. It is a shape that does not consist of a single corner or edge. It is completely round. One crucial aspect of a sphere is the radius. Radius is always required to construct a sphere. The surface of the sphere is always at an equal distance from its center. This distance is known as the radius and is very useful in calculating the surface area of the sphere. One will get the diameter of the circle if the radius of the sphere is multiplied by a factor of two.
The surface area of a sphere:
To calculate the surface area of sphere, we just need to know one value and that is the radius of the sphere or the diameter of the sphere. 4πr2 is the formula used to calculate the surface area of the sphere, where r is the radius of the given sphere. It can be represented in terms of diameter as 4π(d/2)2, here diameter is denoted by d. It is one of the easiest methods of calculating the surface area of a sphere. Every student should know these basic formulas used in everyday life to calculate the surface area of various shapes.
In the above article, we have discussed the surface area of the sphere and cone in detail. Such mathematical concepts are crucial to be understood by students because of their applications. Students can take help from Cuemath for understanding such mathematical concepts. Cuemath is an excellent platform to learn concepts related to math and coding.
