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The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. What is the surface area of the cuboid?

288 sq.cm
216 sq.cm
144 sq.cm
Cannot be determined due to insufficient data

Correct Answer: 288 sq.cm

Explanation:

Let lengths, breadth and height of cuboid be l, b and h respectively

According to question

l+b+h = 22cm......(i)

and

√(l^2+b^2+h^2) = 14cm .....(ii)

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

Squaring eq (i) gives

l 2 + b 2 + h 2

+ 2(lb+bh+lh) = 484

Substituting l^2+b^2+h^2 from eq (i)

2(lb+bh+lh) = 484 -196 = 288 sq.cm

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