A cuboid's length, breadth, and depth sum to 19 cm, with a diagonal of 5√5 cm. What is its surface area_________?
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Answer: B. 236 Sq.cm
Explanation
Squaring the sum of the three linear dimensions gives the expansion containing both surface area and diagonal terms. Squaring the given diagonal length yields the sum of the squared dimensions equal to one hundred twenty-five. Subtracting the sum of squared dimensions from the squared sum of dimensions leaves a total surface area of 236 square centimeters. The square of the sum of three variables equals the sum of their squares plus twice all pairwise products. The total surface area of a rectangular cuboid is given by twice the sum of the products of its dimensions. The internal space diagonal of a cuboid equals the square root of the sum of the squared length, breadth, and depth.
Option A represents an incomplete calculation that only accounts for a portion of the total cuboid surface area. Option C represents the squared sum of the dimensions before subtracting the internal diagonal squared value. Option D is incorrect because option B successfully provides the correct mathematical answer.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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