7th Grade Math Surface Area and Volume

In geometry, surface area and volume are the quantitative measures of various 3D shapes or objects. Surface area of any 3D shape represents the area it occupies. Whereas the volume is the measure of the capacity of any 3D object or space occupied by it. 

The surface area and volume formulas are used to measure any shape’s surface area in square units and the volume in cubic units. 

Important points of the Surface Area And Volume


  • There are two types of 3D shapes, one with only flat surfaces and other one with curved surfaces. 
  • Surface area of shapes with curved surface is sum of its curved surface area and flat surface area. 
  • The curved surface area is also known as lateral surface area (LSA). 
  • The sum of curved surface area and flat surface area is called total surface area (TSA). 


  • For example, TSA of a cylinder = 2 π r(r+h) and LSA = 2πrh.
  •  Volume of Cylinder = π r2 h. Where r is the radius of its circular base and h is its height. 


Surface Area and Volume examples


  1. Find the Surface area of a cubical box having dimensions 4 cm, 2 cm and 5 cm. 

Let length = 4, breadth = 2, and height = 5.

Surface Area of Cuboid = 2(lb + bh + hl) = 2(4*2 + 2*5 + 5*4) = 2(8+10+20) = 2(38) = 76 sq. cm. 


  1. Calculate the volume of a cylindrical pipe with base radii 2 m and height 10 m.

Radius of base = 2 m

Height of cylinder = 10 m

Let π = 3.14

Volume of Cylinder = πr2h = 3.14 * (2)2 * 10 = 3.14 * 4 * 10 = 125.6 cu. Meter. 


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Sum up 


Measuring volume and surface area grade 7 is an important concept of geometry. They are basic mathematical concepts that students must understand in detail. 


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