Surface Area and Volume Formula: Surface Area and Volume calculation is an important part of the curriculum for Maths students. Right from grades 5 and 6, students are taught to calculate area and perimeter for squares, rectangles and c
Surface Area Definition
The area covered by the surface of an object is called its surface area.
Surface area is measured in square units.
Surface area is of two types:
Curved Surface Area CSA or Lateral Surface Area
Curved Surface area is the space occupied by the curved surface of a solid. The base is not considered.
Total Surface Area TSA
The total surface area of an object is the area of its base and the curved surface as well.
Therefore, TSA = Area of base + Area of the curved surface
Volume Definition
The amount of space covered by an object is called its volume.
Volume is measured in cubic units.
Surface Area and Volume of Cube
When Length = Breadth = Height = a:
Cube Surface Area Formula
Curved surface area of a cube formula = 4a2
Total surface area of a cube formula= 6a2
Cube Volume Formula
Volume of a cube= a3
Surface Area and Volume of Cone
If Radius = r, Height = h and Slant Height = l
Cone Surface Area Formula
Curved surface area of a cone formula = πrl
Total surface area of a cone formula = πrl + πr2 = πr(r + l)
Cone Volume Formula
Volume of a cone formula = 1/3 x πr2h
Surface Area and Volume of Cuboid
When Length = l, Breadth = b, Height = h
Cuboid Surface Area Formula
Curved surface area of a cuboid formula = 2(lh + bh) = 2(l + b)h
Total surface area of a cuboid formula = 2(lb + bh + lh)
Cuboid Volume Formula
Volume of a cuboid formula = l x b x h
Surface Area and Volume of Cylinder
When Radius = r and Height = h:
Cylinder Surface Area Formula
Curved surface area of a cylinder formula = 2πrh
Total surface area of a cylinder formula = 2πrh + πr2 + πr2 = 2πrh + 2πr2 = 2πr(r + h)
Cylinder Volume Formula
Volume of a cylinder formula = πr2h
Surface Area and Volume of Frustum
When,
Radius of top circular part = r1
Radius of bottom circular part = r2
Height = h
Slant height = l
Frustum Surface Area Formula
Curved surface area of a frustum formula = π(r1+r2)l
Total surface area of a frustum formula = π(r1+r2)l + πr12 + πr22
Frustum Volume Formula
Volume of a frustum formula = 1/3 (πh(πr12 + πr22+ r1r2)
Surface Area and Volume of Hemisphere
Take Radius = r,
Hemisphere Surface Area Formula
Curved surface area of a hemisphere formula = 2πr2
Total surface area of a hemisphere formula = 2πr2 + πr2 = 3πr2
Hemisphere Volume Formula
Volume of a hemisphere formula = 2/3 (πr3)
Surface Area and Volume of Sphere
Here, Radius = r
Sphere Surface Area Formula
Total surface area of a sphere formula = 4πr2
Sphere Volume Formula
Volume of a sphere formula = 4/3 (πr3)
Surface Area and Volume Formula List
| Shape | Lateral / Curved Surface Area (Square Units) | Total Surface Area (Square units) | Volume (Cubic units) |
| Cube | LSA = 4l2 | TSA = 6l2 | V = l3 |
| Cone | CSA = πrl | TSA = πr(l + r) | V = (1/3)πr2h |
| Cuboid | LSA = 2h(l + b) | TSA = 2(lb + bh + lh) | V = l × b × h |
| Cylinder | CSA = 2π × r × h | TSA = 2πr(h + r) | V = πr2h |
| Frustum | CSA = π(r1+r2)l | TSA = π(r1 + r2)l + π(r12 + r22) | V = (1/3)πh(r12 + r22 + r1r2) |
| Hemisphere | CSA = 2πr2 | TSA = 3πr2 | V = (2/3)πr3 |
| Sphere | CSA = TSA = 4πr2 | TSA = CSA = 4πr2 | V = (4/3)πr3 |
Surface Area and Volume Solved Examples
Que 1: Find the lateral surface area of a cylinder with a base radius of 10 cm and height 20 cm.
Solution:
Given radius r = 10, height h = 20
LSA = 2πrh
= 2 * π* 10 * 20
= 400π
= 400 x 3.14
= 1256.7
The LSA of given cylinder is 1256.7 cm2 or 12.5 m2
Que 2: Find the total surface area and volume of a cuboid with length 5 cm, breadth 4 cm and height 3 cm.
Solution:
Given length 5 cm, breadth 4 cm and height 3 cm
TSA = 2(lb + bh + lh)
= 2(5*4 + 4*3 + 5*3)
= 2(20 + 12 + 15)
= 2 * 47
= 94 cm2
Volume = l × b × h
= 5 * 4 * 3
= 60 cm3
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