Question 2

2X10⁴

To find the number of medium-sized sand grains that can be lined up to make a total length of 1 meter, we first calculate the volume of a single grain approximated as a cube with an edge length of 5X10⁻⁴ meters. The volume is (5X10⁻⁴)³, and we find the number of grains in 1 meter by dividing 1 meter by the edge length.

A) 2X10³

This option is incorrect because it underestimates the number of grains that fit into 1 meter. When calculating the number of grains, the division yields a greater value than what is represented by this expression.

B) 2X10⁴

This is the correct answer. After calculating the total number of grains that can fit in 1 meter by taking the inverse of the edge length (1 / (5X10⁻⁴)), we find that the expression simplifies to 2X10⁴, indicating that this many grains can be lined up side by side.

C) 2X10⁵

This option is also incorrect as it suggests an even larger number of grains than actually fits in 1 meter. The calculation shows that the number of grains is significantly lower than this value, indicating a miscalculation.

D) 5X10³

This choice is incorrect because it is too low. The calculation shows that the total length achievable by 5X10³ grains would not equal 1 meter, indicating that it does not accurately reflect the number of grains that can fit.

E) 5X10⁴

This option is incorrect as it overestimates the number of grains that can be lined up to make 1 meter. The correct calculations lead to a lower total than this expression suggests.

Conclusion

The correct answer, 2X10⁴, accurately reflects the number of medium-sized sand grains that can be lined up to equal 1 meter, based on the calculations derived from the grain's edge length. All other options fail to represent the correct calculation, either by underestimating or overestimating the total number of grains that fit into the specified length.