To determine the new surface area when all dimensions of a rectangular prism are doubled, follow these steps:
1. Identify the Scaling Factor:
When all dimensions of a rectangular prism are doubled, each linear dimension (length, width, and height) is multiplied by 2.
2. Understand How Surface Area Changes:
Surface area is a two-dimensional measure. When each linear dimension of a shape is scaled by a factor of 2, the surface area changes by the square of the scaling factor. In this case, the scaling factor is 2, so the surface area will increase by [tex]\(2^2 = 4\)[/tex].
3. Calculate the New Surface Area:
Multiply the original surface area by 4 to get the new surface area.
So, given the original surface area of the rectangular prism is 450 square meters, the calculation will be:
[tex]\[
450 \, \text{m}^2 \times 4 = 1800 \, \text{m}^2
\][/tex]
Therefore, the new surface area of the rectangular prism, after doubling all its dimensions, is [tex]\(1800\)[/tex] square meters.
