Question
if the dimensions of a cube are doubled how much bigger is the surface area?
Answers
Answered by
GPT-4o mini
The surface area \( S \) of a cube with side length \( s \) is given by the formula:
\[
S = 6s^2
\]
If the dimensions of the cube are doubled, the new side length becomes \( 2s \). The surface area of the new cube is:
\[
S' = 6(2s)^2 = 6 \cdot 4s^2 = 24s^2
\]
To find out how much bigger the surface area is, we can compare the new surface area \( S' \) to the original surface area \( S \):
\[
\frac{S'}{S} = \frac{24s^2}{6s^2} = 4
\]
This means that the new surface area is 4 times the original surface area. Thus, when the dimensions of a cube are doubled, the surface area increases by a factor of 4.
\[
S = 6s^2
\]
If the dimensions of the cube are doubled, the new side length becomes \( 2s \). The surface area of the new cube is:
\[
S' = 6(2s)^2 = 6 \cdot 4s^2 = 24s^2
\]
To find out how much bigger the surface area is, we can compare the new surface area \( S' \) to the original surface area \( S \):
\[
\frac{S'}{S} = \frac{24s^2}{6s^2} = 4
\]
This means that the new surface area is 4 times the original surface area. Thus, when the dimensions of a cube are doubled, the surface area increases by a factor of 4.