Question : A cuboid with sides 4, 6, and 8 units is covered with paper. The paper is removed and a square is made from it. What is the side (in units) of the square?
Option 1: 12.24
Option 2: 16.62
Option 3: 14.42
Option 4: 12.62
Correct Answer: 14.42
Solution :
The total surface area of cuboid $= 2(lb+bh+hl)$ where $l$ is the length, $b$ is the breadth, and $h$ is the height of the cuboid.
Area of square = $(\text{side})^2$
According to the question,
The paper used for covering the cuboid is removed and a square is made.
So, the total surface area of the cuboid = Area of the square
⇒ $2(lb+bh+hl) = (\text{side})^2$
⇒ $2(4\times 6 +6\times 8+8\times 4)=(\text{side})^2$
⇒ $2(24+48+32)=(\text{side})^2$
⇒ $2(104)= (\text{side})^2$
⇒ $\text{side}=\sqrt{208}=14.42\ \mathrm{cm}$
Hence, the correct answer is 14.42.
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