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



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(1) If a cuboid has length l, breadth b and height h,then
(i)  Perimeter of the cuboid  = 4 (L + b + h)
For Example: 
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: 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: 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   = \sqrt {{l^2} + {b^2} + {h^2}}
For Example: If l = 5cm,b = 2cm,h = 3cm ,then
Length of a diagonal   = \sqrt {{5^2} + {2^2} + {3^2}} = \sqrt {38}cm

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

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(2)If the length of each edge of a cube is l, then
(i) Perimeter of the cuboid  = 12l = 12(Edge)
For Example: 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: 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: 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: If l = 5cm,b = 2cm,h = 3cm ,then
Volume of the cuboid  = {5^3} = 125c{m^3}

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