Question : The sum of the length and breadth of a cuboid is 4 cm. Length is three times the breadth. If the height of the cuboid is half of the sum of its length and breadth. Then what is the total surface area of the cuboid?
Option 1: 64 cm2
Option 2: 22 cm2
Option 3: 32 cm2
Option 4: 30 cm2
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Correct Answer: 22 cm 2
Solution :
Given:
The sum of length and breadth = 4 cm
Length = 3 times of breadth
Height = half of the sum of length and breadth
Let breadth = $x$
⇒ Length = $3x$
⇒ Sum of length and breadth = $x + 3x = 4x$
Also, Sum of length and breadth = 4 cm
⇒ $4x=4$
⇒ $x = 1$
Height = $\frac{1}{2} ×$ (Length + Breadth) = $\frac{1}{2} ×$4 = 2 cm
So, the total surface area $=2[(3×1) + (1×2) + (2×3)] = 2(3 + 2 + 6) = 2 × 11 = 22$ cm$^2$
Hence, the correct answer is 22 cm
2
.
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