Compare the surface area of a rectangular solid that is 2 inches by 4 inches by 7 inches to the surface area of a rectangular solid whose dimensions are double those of the first one.

Question

Compare the surface area of a rectangular solid that is 2 inches by 4 inches by 7 inches to the surface area of a rectangular solid whose dimensions are double those of the first one. Explain your reasons

Answer 1

Information from Raymond is correct

Answer 2

surface area of a rectangular solid has 6 sides, 2 are 2x4, 2 are 4x7 and the other 2 are 2x7

that adds up to 2(8+28+14) = 100 square inches

double each side gives 2 sides of 4x8, two of 8x14 and two of 4x14

they add up to 2(32+112+56) = 400 square inches

double each dimension and you quadruple the surface area

Look at a simple square, 1 inch by 1 inch. It has area = 1x1 = 1 square inch

then double its dimensions to get 2 inches by 2 inches. It's area is 4 square inches, 2 x 2 = 4

you go from 1 to 4 in area,

If you tripled the dimensions, you'd increase the area by a factor of 9 = 3^2