How to Measure the Surface Area of Different Geometrical Shapes?

How to Measure the Surface Area of Different Geometrical Shapes?

In Geometry, the two different measurements used to define the three-dimensional objects are the surface area and the volume. The surface area is the total area that the surface of the three-dimensional object occupies. The volume is the total space occupied by the solid object. Let us discuss the classification of surface area, how to measure the surface area for different geometrical shapes in this article.

Classification of Surface Area

The surface area is classified into different types. They are:

  • Curved Surface Area  (CSA)
  • Lateral Surface Area (LSA)
  • Total Surface Area (TSA)

Curved Surface Area (CSA) is the area of all the curved surface of the object. Lateral Surface Area (LSA) is the area of all the lateral surface area of the object except the top and base area. In the case of cylinder and hemisphere, the curved surface area of a cylinder, and hemisphere is the same as LSA of cylinder and hemisphere. Total Surface Area (TSA) is the area of all the surfaces of the object. 

How to Measure Surface Area?

Let us consider an example for finding the cylinder surface area:

A cylinder is a three-dimensional shape which is made up of two similar measure circles and a rectangle, in which the bottom is the boundary of the circle.

To find the surface area, we should add the surface area of two circles and a rectangle.

We know that the area of a circle is πr2 square units.

Since we have two circles on the top and bottom, the area can be calculated as

Area of top and bottom = πr2 + πr2 = 2πr2.

Therefore, the area of the bases is 2πr2 square units.

Next is to find the cylinder curved surface area. 

Since, a rectangle whose base is the circumference of a circle, and h be the height, then the formula for the surface area of a rectangle in terms of cylinder curved surface area is given as:

CSA = 2πrh square units.

Therefore, the total surface area is given as the curved surface area and the area of the bases

TSA = 2πrh+  2πr2

TSA = 2πr (h +r)  square units

Therefore, TSA of a cylinder is  2πr (h +r)  square units

In this way, we can find the surface area of all the solid geometrical shapes such as prism, pyramid, cone, cube, and cuboid.

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