Question

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The sum of length, breadth and height of a cuboid is 38 cm and the lengths of its diagonal is 22 cm. Find the total surface area of the cuboid (in cm2).

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Answer 1

Answer:

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Step-by-step explanation:

Solution.

Let length, breadth and height of the cuboid be l cm, b cm and h cm, respectively.

Given:

l + b + h = 38 cm 

and diagonal = 22 cm.

Surface area of cuboid = 2(lh+ lb+ bh)

                                  = (l+b+h)² - (l²+b²+h²)

                                  = 38² - 22²

                                  = 960

Surface area of cuboid is 960 cm²

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Answer 2

Answer:

given : L+B+H = 38 cm

length of the diagonal D = 22 cm

to find CSA

D = √(L²+B²+H²)

22 = √(L²+B²+H²)

=> 484 = L²+B²+H²

therefore L²+B²+H² = 484 , L+B+H = 38 cm

CSA = 2(LH + BH + LB).........1

(L+B+H)² = L²+B²+H²+ [2(LH+BH+LB)]

38² = 484 + TSA ( from 1)

therefore TSA = 38² - 484

=> TSA = 1444 - 485

=> TSA = 960 cm²