Multiple choice

A closed box is built of wood of uniform thickness. Its external dimensions are 12 cm, 10 cm and 8 cm. If the inner surface area is 376 square cm, then what is the thickness of the wood?

  1. 0.5 cm

  2. 1 cm

  3. 1.5 cm

  4. 2 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let thickness be x. Inner dimensions are (12-2x), (10-2x), (8-2x). Inner surface area = 2 * [(12-2x)(10-2x) + (10-2x)(8-2x) + (12-2x)(8-2x)] = 376. Dividing by 2: (120 - 44x + 4x^2) + (80 - 36x + 4x^2) + (96 - 40x + 4x^2) = 188. 12x^2 - 120x + 296 = 188. 12x^2 - 120x + 108 = 0. x^2 - 10x + 9 = 0. (x-1)(x-9) = 0. x=1.

AI explanation

Let the uniform thickness of the wood be x, making the inner dimensions (12-2x), (10-2x), and (8-2x) cm. Using the total inner surface area formula for a cuboid, 2*((12-2x)(10-2x) + (12-2x)(8-2x) + (10-2x)(8-2x)) = 376. Testing the given options, substituting x = 1 cm yields inner dimensions of 10 cm by 8 cm by 6 cm, and applying the surface area formula gives 2*(80 + 60 + 48) = 2*188 = 376 square cm, confirming the thickness is 1 cm.

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