Total Surface Area of a Cuboid

Total Surface Area of a Cuboid: 

Total surface area of cuboid= ,   where,

l is the length of cuboid,  b is the breadth of cuboid and h is the height of the cuboid.

Illustration: An indoor greenhouse is made entirely of glass panes held together with tape. It is 30cm long, 25cm wide, and 25cm height. Find the area of the glass?

Solution: We have, Length=30cm, Breadth=25cm and Height=25cm

Area of glass = Total surface area of cuboid =  

                                                              = 2 (30 x 25 + 25 x 25 + 30 x 25) 

                                                             = 2(750 + 625 + 750) 

                                                            = 

Illustration: A plastic box 1.5 m long, 1.25 m wide and 65 cm deep is to be made. It is to be open at the top. Ignoring the thickness of the plastic sheet, determine:

(i) The area of the sheet required for making the box.

(ii) The cost of the sheet for it, if a sheet measuring costs Rs 20.

Solution: We have,

l = Length of plastic box = 1.5 m

b = Breradth of plastic box = 1.25 m

h = height of plastic box = 65 cm = 65/100 = 0.65 m

Total surface area of the plastic box = lb + 2(bh + hl)

                                                   =

Hence the area of the sheet required for making the box is 

(ii) Since sheet costs Rs 20. Therefore,

Cost of sheet required for making the box = Area of the sheet X Rate per sq. metre

                                                            = Rs (5.45 X 20)

                                                            = Rs 109