Surface Areas and Volumes
Basics
Cuboid and Its Surface Area
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces. Consider a
cuboid whose dimensions are l × b × h respectively.
Total surface area of cuboid(TSA) = Sum of the areas of all its six faces TSA
(cuboid) = 2(l × b) + 2(b × h) + 2(l × h) = 2(lb + bh + lh)
Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces. The lateral
surface area of the cuboid = Area of face AEHD + Area of face BFGC + Area of face ABFE + Area
of face DHGC
LSA (cuboid) = 2(b × h) + 2(l × h) = 2h(l + b)
Length of diagonal of a cuboid =
, Cube and Its Surface Area
For a cube length = breadth = height
TSA (cube) = 2 × (3l 2) = 6l2
Similarly, the Lateral surface area of cube = 2(l × l + l × l) = 4l2
Note: Diagonal of a cube = √3l
Cylinder and Its Surface Area
Take a cylinder of base radius r and height h units. The curved surface of this cylinder, if opened along
the diameter (d = 2r) of the circular base can be transformed into a rectangle of length 2πr and height
h units. Thus,
Basics
Cuboid and Its Surface Area
The surface area of a cuboid is equal to the sum of the areas of its six rectangular faces. Consider a
cuboid whose dimensions are l × b × h respectively.
Total surface area of cuboid(TSA) = Sum of the areas of all its six faces TSA
(cuboid) = 2(l × b) + 2(b × h) + 2(l × h) = 2(lb + bh + lh)
Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces. The lateral
surface area of the cuboid = Area of face AEHD + Area of face BFGC + Area of face ABFE + Area
of face DHGC
LSA (cuboid) = 2(b × h) + 2(l × h) = 2h(l + b)
Length of diagonal of a cuboid =
, Cube and Its Surface Area
For a cube length = breadth = height
TSA (cube) = 2 × (3l 2) = 6l2
Similarly, the Lateral surface area of cube = 2(l × l + l × l) = 4l2
Note: Diagonal of a cube = √3l
Cylinder and Its Surface Area
Take a cylinder of base radius r and height h units. The curved surface of this cylinder, if opened along
the diameter (d = 2r) of the circular base can be transformed into a rectangle of length 2πr and height
h units. Thus,
