The volumes of two similar solids are 216 ft and 1331 ft. The surface area of the smaller solid is 180 ft. What is the surface area of the larger solid?

Answer 1

180 ft^2 * (1311 / 216)^2
for similar things
area goes as L^2
volume as L^3

Answer 2

volumes of similar shapes are proportional to the cubes of their corresponding sides
so 216 : 1331 = side1^3/side2^3
side1 : side2 = 6 : 11

the areas of similar shapes are proportional to the square of their corresponding sides
180 : x = 6^2 : 11^2
180/x = 36/121
36x = 21780
x = 605

The larger has a surface area of 605 ft^2

Answer 3

Thank you.