Question

Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 \(cm^2\).
Reason (R) : The surface area of a cuboid of dimensions \(l \times b \times h\) is \((lb + bh + hl)\).

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
• B. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

Pay close attention to formulas in the Reason statements of Assertion-Reason questions.
Often, a standard formula is slightly modified (such as missing a factor of 2 or a square root) to test your attention to detail.
Identifying incorrect formulas immediately helps you eliminate options and find the correct answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is an Assertion-Reason type question.
We need to independently evaluate the mathematical truth of both the Assertion (A) and the Reason (R) statements and determine their logical connection.

Step 2: Key Formula or Approach:
1. The total surface area of a cuboid with length \(l\), breadth \(b\), and height \(h\) is:
\[ \text{TSA}_{\text{cuboid}} = 2(lb + bh + hl) \]
2. When two identical cubes of side \(s\) are joined end-to-end, they form a cuboid where:
Length, \(l = 2s\)
Breadth, \(b = s\)
Height, \(h = s\)

Step 3: Detailed Explanation:
1. Evaluate Assertion (A):
- Two cubes of side \(s = 4\text{ cm}\) are joined end-to-end.
- The resulting cuboid will have dimensions:
\[ l = 4 + 4 = 8\text{ cm} \]
\[ b = 4\text{ cm} \]
\[ h = 4\text{ cm} \]
- Calculate its total surface area:
\[ \text{TSA} = 2(lb + bh + hl) \]
\[ \text{TSA} = 2(8 \times 4 + 4 \times 4 + 4 \times 8) \]
\[ \text{TSA} = 2(32 + 16 + 32) \]
\[ \text{TSA} = 2(80) = 160\text{ cm}^2 \]
- The Assertion states that the surface area is \(160\text{ cm}^2\). This is mathematically correct.
- Therefore, Assertion (A) is True.
2. Evaluate Reason (R):
- The statement claims that the surface area of a cuboid of dimensions \(l \times b \times h\) is \((lb + bh + hl)\).
- This is incorrect because the standard formula for the total surface area of a cuboid is \(2(lb + bh + hl)\).
- It is missing the factor of 2.
- Therefore, Reason (R) is False.

Step 4: Final Answer:
Since Assertion (A) is true but Reason (R) is false, the correct option is (C).