You are given below a question followed by two statements I and II. You have…

2023

You are given below a question followed by two statements I and II. You have to decide whether the data provided in the statements is/are sufficient to answer the question. Find the surface area of a cuboid. Statement I:The sum of the length, the breadth and the depth of a cuboid is 20 cm. Statement II: Diagonal of the cuboid is 5sqrt{5} cm.

  1. A.

    If data in statement I alone is sufficient to answer the question

  2. B.

    If data in statement II alone is sufficient to answer the question

  3. C.

    If data in both the statements I & II together are necessary to answer the question

  4. D.

    If data in both the statements I & II together are not sufficient to answer the question

  5. E.

    Question not attempted

Attempted by 38 students.

Show answer & explanation

Correct answer: C

To determine if the provided statements are sufficient to find the surface area of a cuboid, let us first identify the formulas involved.

For a cuboid with length l, breadth b, and height (depth) h:

Total Surface Area (TSA): 2 * (lb + bh + hl)

Diagonal: Square root of (l * l + b * b + h * h)

Step-by-Step Analysis
Analyze Statement I: "The sum of the length, the breadth and the depth of a cuboid is 20 cm."

This gives us: l + b + h = 20.

This statement alone is insufficient because it does not provide information about individual dimensions or their pairwise products (lb, bh, hl).

Analyze Statement II: "Diagonal of the cuboid is 5 * square root of 5 cm."

This gives us: Square root of (l * l + b * b + h * h) = 5 * square root of 5.

Squaring both sides: l * l + b * b + h * h = 125.

This statement alone is insufficient because it provides no information about the individual dimensions or the surface area.

Analyze Statements I and II together:

From Statement I, we have l + b + h = 20. Squaring both sides: (l + b + h) * (l + b + h) = 20 * 20 = 400.

Expanding this gives: (l * l + b * b + h * h) + 2 * (lb + bh + hl) = 400.

From Statement II, we know l * l + b * b + h * h = 125.

Substituting this into the equation: 125 + 2 * (lb + bh + hl) = 400.

2 * (lb + bh + hl) = 400 - 125 = 275 square cm.

Since 2 * (lb + bh + hl) is the formula for the Total Surface Area, we have found the answer by using both statements together.

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