Surface Area Definition, Formulas & Worksheet!

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Learn everything from definition of Surface Area to formulas:


What is Surface Area?

Surface area is defined as the surface size of any object. We have different shapes with different surface areas.

What is Area?

Area is defined as the size of any object. Area is measured in square units. Some of the units of area are centimeter square, meter square, feet square, inches square, etc.

What is Lateral Surface Area?

Lateral surface area is defined as the side surface area of an object.


What are the formulas to calculate volume of common shapes around us: 


Square:- Square is a shape which has four equal sides and all the angles are right angles as shown in figure below.



The area of square is given by formula:-                                                                                                                                                                                                                         

                                                 Area =  length × length

Rectangle:-Rectangle is a shape which has four equal and opposite sides and all the angle are right angles.



The area of rectangle is given by formula:-

                    Area =  length × breadth

Triangle:-  Triangle is a shape having three sides.                                               

The area of triangle is given by the formula:

                                    Area =  12 (base × height)

Circle:- Area of circle can be given as under:-

                                           Area = πr^2


Cylinder:- The area of square is given by formula:-


                      Total Surface Area =  2πr(r+h)


                       Lateral Surface area = 2πrh


Cone:-  Area of cone is given by the formula:-                                          

                                Total Surface Area= r+h^2+r^2

                              Lateral Surface Area = rh^2+r^2


Sphere:- Area of sphere is given by:-                                                                      

                                             Area = 4πr^2



Surface Area Questions & Answers - Sample

Que 1:- What is the area of the square having sides 3m ?

Ans   Length of side of square = 3 m 

          Area of square =  length × length

                                      = 3 × 3 = 9 m^2

Que 2 :- What is the radius of the sphere having area 16 m2?

  Ans  Area of sphere = 16 m^2

           As area of sphere = 4πr^2   

                        4πr^2=  16                         ^                                                             

                        r^2= 4

                        r = 2 m

Thus, the radius of the sphere is 2m

Que 3:- What is the lateral and total surface area of the cylinder having height  4cm and radius 2 cm ?

Ans  Height of cylinder , h = 4 cm

        Radius of cylinder , r = 2 cm 

        Total surface of area =  2πr(r+h) = 2π^2 (2+4)

                                = 24πcm^2

Say no to Surface Area Homework Stress and Yes to A+ Grades

The Concept of surface area was introduced to students around the United States during the middle school years. Students are taught how to calculate and solve problems related to any three-dimensional geometrical shapes.

Just like the topic of volume, students learning the details about three dimensional shapes deal with complex topics like different shapes have different surface areas. 

The topic of surface area can be many times confused with the volume and hence get a student confused. Therefore it is essential to get the correct guidance so that students from the very early on understand the differences between the two topics as well as feel confident solving homework questions or even attempting surface area questions in their exams. 

Surface area is one of those concepts that has a lot of real life application in our day to day life. One needs surface area to figure out the amount of frosting needed for a birthday cake, we can use surface area of a cylinder to understand the amount of paint needed for a cylindrical fuel tank, we can even find applications of surface area and its formulas in marketing role such as based on the dimensions of the object how big should the label be for the box. 

We have designed our help to meet study needs of students around the clock. We have some of the best math experts to help your child with the  core concepts of surface area. 

Available 24/7, our tutors can handle all surface area related questions and get you the correct solutions at the most reasonable prices.


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