# Surface Area and Volume of a Cuboid and Cube - Class 9 : Notes

(1) If a cuboid has length l, breadth b and height h,then
(i)Â  Perimeter of the cuboid Â = 4 (L + b + h)
For Example:Â
If $l = 5cm,b = 2cm,h = 3cm$ ,then
Perimeter of the cuboid $= 4\left( {5 + 2 + 3} \right) = 40cm$

(ii) Surface area of the cuboid $= 2\left( {lb + bh + lh} \right)$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Surface area of the cuboid $= 2\left( {5 \times 2 + 2 \times 3 + 5 \times 3} \right) = 62c{m^2}$

(iii) Lateral surface area of the cuboid $= 2(l + b) \times h$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Lateral surface area of the cuboid $= 2(5 + 2) \times 3 = 42c{m^2}$

(iv) Length of a diagonal Â $= \sqrt {{l^2} + {b^2} + {h^2}}$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Length of a diagonal Â $= \sqrt {{5^2} + {2^2} + {3^2}} = \sqrt {38}cm$

(v) Volume of the cuboid $= l \times b \times h$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Volume of the cuboid $= 5 \times 2 \times 3 = 30c{m^3}$

(2)If the length of each edge of a cube is l, then
(i) Perimeter of the cuboid $= 12l = 12(Edge)$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Perimeter of the cuboid $= 12 \times 5 = 60cm$

(ii) Surface area of the cuboid $= 6{l^2} = 6{(Edge)^2}$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Surface area of the cuboid $= {\left( {6 \times 5} \right)^2} = 900c{m^2}$

(iii) Lateral surface area of the cuboid $= 4{l^2} = 4{(Edge)^2}$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Lateral surface area of the cuboid $= {\left( {4 \times 5} \right)^2} = 400c{m^2}$

(iv) Volume of the cuboid $= {l^3} = {(Edge)^3}$
For Example:Â If $l = 5cm,b = 2cm,h = 3cm$ ,then
Volume of the cuboid $= {5^3} = 125c{m^3}$