The volume of a rectangular solid with length 8, width 6, and height 4 is how many times the volume of a rectangular solid with length 4, width 3, and height 2?

Answer

To solve the problem, we will calculate the volumes of both rectangular solids and then determine how many times the volume of the first solid is compared to the second solid.

### Step 1: Calculate the volume of the first rectangular solid.
The formula for the volume \( V \) of a rectangular solid (cuboid) is given by:
\[ V = \text{length} \times \text{width} \times \text{height} \]

For the first solid:
- Length = 8
- Width = 6
- Height = 4

Substituting these values into the formula:
\[ V_1 = 8 \times 6 \times 4 \]

Calculating this:
\[ V_1 = 48 \times 4 = 192 \]

### Step 2: Calculate the volume of the second rectangular solid.
Using the same volume formula for the second solid:
- Length = 4
- Width = 3
- Height = 2

Substituting these values into the formula:
\[ V_2 = 4 \times 3 \times 2 \]

Calculating this:
\[ V_2 = 12 \times 2 = 24 \]

### Step 3: Determine how many times the volume of the first solid is compared to the second solid.
To find how many times the volume of the first solid is compared to the second solid, we divide the volume of the first solid by the volume of the second solid:
\[ \text{Ratio} = \frac{V_1}{V_2} = \frac{192}{24} \]

Calculating this:
\[ \text{Ratio} = 8 \]

### Final Answer:
The volume of the first rectangular solid is 8 times the volume of the second rectangular solid.

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