Question

If there is an error of \( k% \) in measuring the edge of a cube, then the percent error in estimating its volume is:

• A. \( k \)
• B. \( 3k \)
• C. \( \frac{k}{3} \)
• D. None of these

Hint:

For volume calculations, the percentage error is multiplied by the power of the exponent. For a cube, this means three times the error in the edge length.

Answer 1

The Correct Option is B

Step 1: Understanding the concept.
The volume of a cube is given by \( V = a^3 \), where \( a \) is the length of the edge of the cube. The percentage error in the volume of a cube is three times the percentage error in the edge length, as volume is directly proportional to the cube of the edge length.
Step 2: Analyzing the options.
- (1) \( k \): This is incorrect because the error in volume is not the same as the error in edge length.
- (2) \( 3k \): This is correct because the error in the volume of a cube is three times the error in the edge length.
- (3) \( \frac{k}{3} \): This is incorrect because the error in volume is not reduced by a factor of three.
- (4) None of these: This is incorrect as option (2) is correct.
Conclusion.
The correct answer is (2) \( 3k \), as the percentage error in the volume is three times the percentage error in the edge length.