Question 6For a volume of 125×125×64125×125×64 which of the following can be used to reduce this to a 125×125×32125×125×32 volume?

1. Break Down the Problem

To reduce the volume from $125 \times 125 \times 64$ to $125 \times 125 \times 32$, we need to analyze the change in dimensions. The original volume is defined by three dimensions, with the third dimension being reduced.

2. Relevant Concepts

The volume formula for a rectangular prism is given by: $\text{Volume} = \text{length} \times \text{width} \times \text{height}$ In this case, we can denote:

• $V_{\text{original}} = 125 \times 125 \times 64$
• $V_{\text{new}} = 125 \times 125 \times 32$

3. Analysis and Detail

Now, let's calculate the original and new volumes:

• Original Volume: $V_{\text{original}} = 125 \times 125 \times 64 = 1,000,000$

• New Volume: $V_{\text{new}} = 125 \times 125 \times 32 = 500,000$

To find the factor by which we can reduce the volume, we can compare the two volumes:

$\text{Reduction Factor} = \frac{V_{\text{original}}}{V_{\text{new}}} = \frac{1,000,000}{500,000} = 2$

4. Verify and Summarize

The original volume needs to be reduced by a factor of 2. This can be accomplished by halving the height (or any equivalent change that maintains the same base area).

By reducing the height from $64$ to $32$, we achieve the desired volume reduction.

Final Answer

To reduce the volume from $125 \times 125 \times 64$ to $125 \times 125 \times 32$, you can halve the height from $64$ to $32$.