Question

Assertion: If the inner dimensions of a cuboidal box are $50cm\times 40cm\times 30cm,$ then the length of the longest rod that can be placed in the box is $50\sqrt{2}cm$.
Reason: The line joining opposite corners of a cuboid is called its diagonal.
Also, length of longest rod $=$ length of diagonal $=\sqrt{l^2+b^2+h^2}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct.

Answer 1

The correct option is A

Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

Length of the diagonal is the length of the longest rod that can be placed in the cuboid.

For cuboid with dimensions, $50cm\times 40cm\times 30cm,$ the length of the diagonal is $\sqrt{{50}^2+{40}^2+{30}^2}=\sqrt{5000}=50\sqrt{2}$

So, both Assertion and Reason are correct and Reason is the correct explanation of Assertion.