Question : The length, breadth, and height of a wooden box with a lid are 10 cm, 9 cm, and 7 cm, respectively. The total inner surface of the closed box is 262 cm2. The thickness of the wood (in cm) is:
Option 1: $2$
Option 2: $3$
Option 3: $\frac{23}{3}$
Option 4: $1$
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Correct Answer: $1$
Solution :
Given: Inner surface area = 262 cm
2
The length, breadth, and height are 10 cm, 9 cm, and 7 cm, respectively.
Let the thickness of the wood be $x$ cm.
Surface area of the cuboid = 2(length × breadth + length × height + breadth × height)
Area of inner surface $= 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10- 2x)(7 - 2x)$
$⇒ 262 = 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10 - 2x)(7- 2x)$
Putting the value of $x = 1,$ the above equation is satisfied.
Hence, the correct answer is $1$.
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