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?

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?

• A. 800 cm³
• B. 1,200 cm³
• C. 5,400 cm³
• D. 1,600 cm³

Answer: (C)

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 =

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 =