MATH SOLVE

4 months ago

Q:
# The previous rectangular prism had a surface area of 254 square inches. If each dimension is doubled, how does the surface area change?The surface area doubles.The surface area triples.The surface area increases by 4 times.The surface area increases by 8 times.

Accepted Solution

A:

Answer:The surface area increases by 4 timesStep-by-step explanation:we know thatIf two figures are similar, then the ratio of its surface areas is equal to the scale factor squaredLetz -----> the scale factorx ----> the surface area of the new rectangular prismy ---> the surface area of the original rectangular prismso[tex]z^{2}=\frac{x}{y}[/tex]we have[tex]z=2[/tex] ----> because is doubled[tex]y=254\ in^{2}[/tex]substitute and solve for x[tex]2^{2}=\frac{x}{254}[/tex][tex]x=(4)254=1,016\ in^{2}[/tex] ----> surface area increases by 4 times.