7th Grade Math Surface Area and Volume

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.