- Identify the given values: volume per cube \(V_s = 4.9 \text{ ml}\) and number of cubes \(N = 1.5 \times 10^6\).
- Use the formula for total volume: \(V_{total} = N \times V_s\).
- Calculate the product of coefficients: \(1.5 \times 4.9 = 7.35\).
- Conclude that the total volume is \(7.35 \times 10^6 \text{ ml}\).
- Final Answer: \(\boxed{7.35 \times 10^6 \text{ ml}}\).
Explanation
- Analysis of the problem
The objective is to determine the total volume of \(1.5 \times 10^6\) sugar cubes, given that each individual cube has a volume of \(4.9 \text{ ml}\). To find the total volume, we multiply the volume of a single sugar cube by the total number of cubes. Let \(V_s = 4.9 \text{ ml}\) be the volume of one cube and \(N = 1.5 \times 10^6\) be the number of cubes. The total volume \(V_{total}\) is given by the formula \(V_{total} = N \times V_s\).
- Calculation of the total volume
We calculate the product:
\[V_{total} = (1.5 \times 10^6) \times 4.9\]
First, multiply the numerical coefficients:
\[1.5 \times 4.9 = 7.35\]
Now, combine this result with the power of 10:
\[V_{total} = 7.35 \times 10^6 \text{ ml}\]
This value matches the first option provided in the problem.
Examples
Calculating the total volume of a substance is common in chemistry and food science. For instance, if you are scaling up a recipe or filling storage containers, knowing the volume per unit and the quantity allows you to determine the required total space. Here, multiplying the volume per cube by the number of cubes helps us understand the aggregate space occupied by millions of sugar cubes.