Geometry is a vital branch of mathematics. Students have to learn various formulas to understand the concepts of geometry properly. Surface area formulas are part of one of the most important topics of geometry. In this topic, students will learn the formulas of lateral and total surface areas of several geometrical shapes. By learning the formulas, students will be able to solve the sums easily. Here, we are going to discuss the surface area formulas of some geometrical shapes. For example, the surface area of a cylinder, surface area of a sphere, etc. are discussed below.
Here, we have given the surface area and volume formulas of different geometrical objects.
The formula for calculating the area of the curved surface of a cylinder or the lateral surface area of a cylinder is 2πrh. The formula for calculating the total surface area of a cylinder is 2πr(r + h). The formula for calculating the volume of a cylinder is πr2h.
The formula for calculating the total surface area of a sphere is 4πr^{2} and for the volume of a sphere is 4/3 πr³.
The formula for calculating the total surface area of a cone is πr(l + r) and for the volume is ⅓ πr2h.
The formula for calculating the lateral surface area of cuboid is 2h(l + b) and for the total surface area is 2(lb + bh + lh).
The formula for calculating the total surface area of a pyramid is (½ × perimeter of base × slant height) + area of the base.
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To score good marks in mathematics exams, students have to learn the formulas of geometry sincerely. They should learn and practice the surface area and volume formulas such as the formula for the surface area of a sphere and memorize them to solve the sums of geometry easily.
1. What are the Different Types of Surface Areas?
Ans: Different geometrical objects have different surface areas such as curved, lateral, or total surface areas. A sphere has only one curved surface area, which is also the total surface area. For any cylinder, cone, cuboid, or pyramid, there are curved or lateral surfaces and plane surfaces. The sum of the plane surface area and the curved or lateral surface area is called the total surface area. A cylinder has two planes and one curved surface area. A cone has one curved and one plane surface area. A cuboid has one curved and one plane surface area. A pyramid has one lateral and one or two plane surface areas.
2. Give Some Differences Between Area and Surface Area.
Ans: Here, we have given some major differences between the area and surface area of different geometrical shapes and figures.
Area | Surface Area |
The area is calculated by measuring the faces of the plane objects. | Surface area is calculated by adding the area of all the faces of an object. |
The area measures the size of 2D shapes. | The surface area measures the size of 3D figures. |
Plane figures such as triangle, square, polygon represent the area. | Solid figures such as a sphere, cylinder, cone, pyramid represent the surface area. |
It refers to the measurement of one surface of the shape. | It refers to the measurement of the exposed faces of solid figures. |
3. What is the Difference Between Curved Surface Area and Total Surface Area?
Ans: There are different types of surface areas in different geometrical objects. Curved surface area and total surface area are two of them. Some of the geometrical objects have curved parts along with plane parts. The surface area of those curved parts is called a curved surface area. On the other hand, the total surface area is the sum of all the surface areas of an object. For example, a cylinder has one curved surface area and two plane surface areas. The total surface area of the cylinder is the sum of the curved surface area and two plane surface areas. This is the main difference between curved and total surface area.