If the volume of a rectangular prism is 200 cubic centimeters and its dimensions are tripled, what is the volume of the new prism in cubic centimeters?

To find the volume of the new rectangular prism after tripling its dimensions, it's important to understand how volume scales with dimensions. The volume ( V ) of a rectangular prism is calculated using the formula ( V = \text{length} \times \text{width} \times \text{height} ).

When each dimension of the prism is tripled, the new length, width, and height become ( 3 \times \text{length} ), ( 3 \times \text{width} ), and ( 3 \times \text{height} ), respectively. The volume of the new prism can be computed as follows:

[

V_{\text{new}} = (3 \times \text{length}) \times (3 \times \text{width}) \times (3 \times \text{height}) = 27 \times (\text{length} \times \text{width} \times \text{height})

]

This results in the new volume being 27 times the original volume. Given that the original volume is 200 cubic centimeters, we can calculate the new volume:

[

V_{\text{new}} = 27 \times 200 =