Explanation:

To estimate the 28-day crushing strength of concrete cubes from the 7-day cube strength, we multiply the 7-day cube strength by a factor. This factor is determined by the relationship between the 7-day and 28-day strengths of concrete.

Factors Affecting Concrete Strength:
1. Curing Time: Concrete gains strength over time, and the 28-day strength is considered as the standard measure of concrete strength.
2. Water-Cement Ratio: The water-cement ratio affects the strength of concrete, with a lower ratio generally resulting in higher strength.
3. Aggregate Properties: The properties of the aggregates used in the concrete mix also influence its strength.

Relationship between 7-day and 28-day Strength:
In general, the 7-day strength of concrete is approximately two-thirds of the 28-day strength. This means that if we have the 7-day cube strength, we can estimate the 28-day cube strength by multiplying it by a certain factor.

Factors to Consider:
1. Variability in Concrete Strength: Concrete strength can vary due to several factors such as the quality of materials, mixing and curing techniques, and environmental conditions. Therefore, the relationship between the 7-day and 28-day strengths may not be consistent for all concrete mixes.
2. Safety Margin: It is important to have a safety margin when estimating the 28-day strength based on the 7-day strength. This ensures that the estimated strength is not underestimated, which could lead to structural failures.

Correct Answer:
The correct answer is option 'C' (1.5). This means that the estimated 28-day cube strength is obtained by multiplying the 7-day cube strength by 1.5. This factor takes into account the relationship between the 7-day and 28-day strengths of concrete, as well as provides a safety margin.

Importance of Estimating Concrete Strength:
Estimating the 28-day strength of concrete based on the 7-day strength is crucial in construction projects. It allows engineers and contractors to assess the quality and performance of the concrete early on. Additionally, it helps in making timely decisions regarding the removal of formwork, post-tensioning, and other construction activities.

Overall, the 28-day crushing strength of concrete cubes can be estimated by multiplying the 7-day cube strength by a factor of 1.5. However, it is important to consider the variability in concrete strength and maintain a safety margin to ensure the estimated strength is reliable and safe for use in construction.