CLASS-8
VOLUME & SURFACE AREA OF CUBOID

CUBOID –

A cuboid is a solid figure bounded by six rectangular faces and is three-dimensional. The adjacent faces are mutually perpendicular and the opposite faces have the same dimension. A cuboid has eight vertices (M, N, O, P, Q, R, S, T) and twelve edges (MN, OP, PM, ON, QR, RS, ST, TQ, MQ, PT, NR, OS). The volume of a cuboid is considered the product of its length, breadth, and height. We would like denoting the volume = V, length = l, breadth = b, and height = h. we have the formula such as -

volume (V) = length (l) X breadth (b) X height (h)

So, V = l X b X h


               V                   V                     V

So, l  = ---------- , b = ---------- ,  h = -----------

             b X h               l X h                 b X l

The surface area of a cuboid is considered as the sum of the surface areas of its six rectangular faces, which works out to the following.

As we all know that, area (A) of a rectangle = length (l) X breadth (b) and also know that, every side of a cuboid is a rectangle and the area of a rectangle of every two opposite sides of a cuboid is the same.  

So,  POST = MNRQ =  h X l

      PMQT = ONRS =  b X h

      MNOP = QRST =  l X b

Now, the surface area of the cuboid

= POST + MNRQ + PMQT + ONRS + MNOP + QRST

= hl + hl + bh + bh + lb + lb

=  2(hl + bh + lb)

The lateral surface area or the area of the four walls of a cuboid works out to.

The area of the four walls = perimeter of the floor X height

                              = 2(l + b) X h


Example) The dimensions of a cuboid are 10 cm by 8 cm by 9 cm. find (1) its volume, (2) it's surface area, (3) the surface area of the four walls.

Ans.) Here, l = 10 cm, b = 8 cm, h = 9 cm

(1) the volume of the cuboid = l X b X h 

                               = 10 cm X 8 cm X 9 cm =  720 cmᶟ  (Ans.)

(2) its surface area = 2 (lb + bh + hl)

                      = 2 {(10 X 8) + (8 X 9) + (9 X 10)}

                      =  2 (80 + 72 + 90) 

                      =  2 X 242 = 484 cm²   (Ans.)

(3) Surface area of the four walls = 2 (l + b) X h 

                                      =  2 (10 + 8) X 9     

                                      =  (2 X 18) X 9      

                                      =  36 X 9 =  324 cm²   (Ans.)