Total surface area of a cuboid


 
 
Concept Explanation
 

Total Surface Area of a Cuboid

Total Surface Area of a Cuboid: 

Total surface area of cuboid= large dpi{80} large 2(lb+bh+lh),   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 = large 2(lb+bh+lh) 

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

                                                             = 2(750 + 625 + 750) 

                                                            = large 4250cm^2

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 1 m^{2} 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)

                                                   = {1.5times 1.25+2(1.25times 0.65+0.65times 1.5)}

                                                  ={1.875+2(0.8125+0.975)}

                                                   =(1.875+3.575);m^{2}

                                                    =5.45;m^{2}

Hence the area of the sheet required for making the box is  5.45;m^{2}

(ii) Since 1 m^{2} 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

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If the length, breadth and height of a cuboid are 6 cm, 8 cm and 7 cm respectively, the total surface area of the cuboid is equal to :

Right Option : B
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Explanation
Question : 2

A room measures 4m by 7m and the ceiling is 3m high. A liter of paint covers 25 sq m. How many liters of paint will it take to paint all but not the floor of the room?

Right Option : A
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Explanation
Question : 3

The length, breadth and height of a room are 5m, 4m and 3m respectively . Find the cost of white -washing the walls of the room and the ceiling at the rate of 7.50 per sq m.

Right Option : A
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Explanation
 
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